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In this work, we introduce a new topological index called a general power sum-connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by Y α G = ∑ u v ∈ E G d u d u + d v d v α , where d u and d v represent the degree of vertices u and v , respectively, and α ≥ 1 . A connected graph G is called a k -generalized quasi-tree if there exists a subset V k ⊂ V G of cardinality k such that the graph G − V k is a tree but for any subset V k − 1 ⊂ V G of cardinality k − 1 , the graph G − V k − 1 is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum-connectivity index.
Rui Cheng; Gohar Ali; Gul Rahmat; Muhammad Yasin Khan; Andrea Semanicova-Fenovcikova; Jia-Bao Liu. Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs. Complexity 2021, 2021, 1 -8.
AMA StyleRui Cheng, Gohar Ali, Gul Rahmat, Muhammad Yasin Khan, Andrea Semanicova-Fenovcikova, Jia-Bao Liu. Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs. Complexity. 2021; 2021 ():1-8.
Chicago/Turabian StyleRui Cheng; Gohar Ali; Gul Rahmat; Muhammad Yasin Khan; Andrea Semanicova-Fenovcikova; Jia-Bao Liu. 2021. "Investigation of General Power Sum-Connectivity Index for Some Classes of Extremal Graphs." Complexity 2021, no. : 1-8.
In this article, an algorithm has been established to approximate parametric-parametric, explicit-implicit, and explicit-explicit surface intersection. Foremost, it extracts the characteristic points (boundary and turning points) from the sequence of intersection points and fits an optimal cubic spline curve to these points. Moreover, this paper utilizes genetic algorithm (GA) for optimization of shape parameters in the portrayal of cubic spline so that the error is minimal. The proposed algorithm is demonstrated with different types of surfaces to analyze its robustness and proficiency. In the end, all illustrations show the effectiveness of the algorithm which makes it more influential to resolve all complexities arises during intersection with a minimal error.
Jiwen Gao; Faiza Sarfraz; Misbah Irshad; Jia-Bao Liu. Optimal Intersection Curves for Surfaces. Journal of Mathematics 2021, 2021, 1 -9.
AMA StyleJiwen Gao, Faiza Sarfraz, Misbah Irshad, Jia-Bao Liu. Optimal Intersection Curves for Surfaces. Journal of Mathematics. 2021; 2021 ():1-9.
Chicago/Turabian StyleJiwen Gao; Faiza Sarfraz; Misbah Irshad; Jia-Bao Liu. 2021. "Optimal Intersection Curves for Surfaces." Journal of Mathematics 2021, no. : 1-9.
A vertex w ∈ V H distinguishes (or resolves) two elements (edges or vertices) a , z ∈ V H ∪ E H if d w , a ≠ d w , z . A set W m of vertices in a nontrivial connected graph H is said to be a mixed resolving set for H if every two different elements (edges and vertices) of H are distinguished by at least one vertex of W m . The mixed resolving set with minimum cardinality in H is called the mixed metric dimension (vertex-edge resolvability) of H and denoted by m dim H . The aim of this research is to determine the mixed metric dimension of some wheel graph subdivisions. We specifically analyze and compare the mixed metric, edge metric, and metric dimensions of the graphs obtained after the wheel graphs’ spoke, cycle, and barycentric subdivisions. We also prove that the mixed resolving sets for some of these graphs are independent.
Bao-Hua Xing; Sunny Kumar Sharma; Vijay Kumar Bhat; Hassan Raza; Jia-Bao Liu. The Vertex-Edge Resolvability of Some Wheel-Related Graphs. Journal of Mathematics 2021, 2021, 1 -16.
AMA StyleBao-Hua Xing, Sunny Kumar Sharma, Vijay Kumar Bhat, Hassan Raza, Jia-Bao Liu. The Vertex-Edge Resolvability of Some Wheel-Related Graphs. Journal of Mathematics. 2021; 2021 ():1-16.
Chicago/Turabian StyleBao-Hua Xing; Sunny Kumar Sharma; Vijay Kumar Bhat; Hassan Raza; Jia-Bao Liu. 2021. "The Vertex-Edge Resolvability of Some Wheel-Related Graphs." Journal of Mathematics 2021, no. : 1-16.
Let G = G 1 × G 2 × ⋯ × G m be the strong product of simple, finite connected graphs, and let ϕ : ℕ ⟶ 0 , ∞ be an increasing function. We consider the action of generalized maximal operator M G ϕ on ℓ p spaces. We determine the exact value of ℓ p -quasi-norm of M G ϕ for the case when G is strong product of complete graphs, where 0 < p ≤ 1 . However, lower and upper bounds of ℓ p -norm have been determined when 1 < p < ∞ . Finally, we computed the lower and upper bounds of M G ϕ p when G is strong product of arbitrary graphs, where 0 < p ≤ 1 .
Zaryab Hussain; Ghulam Murtaza; Toqeer Mahmood; Jia-Bao Liu. Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs. Mathematical Problems in Engineering 2021, 2021, 1 -9.
AMA StyleZaryab Hussain, Ghulam Murtaza, Toqeer Mahmood, Jia-Bao Liu. Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs. Mathematical Problems in Engineering. 2021; 2021 ():1-9.
Chicago/Turabian StyleZaryab Hussain; Ghulam Murtaza; Toqeer Mahmood; Jia-Bao Liu. 2021. "Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs." Mathematical Problems in Engineering 2021, no. : 1-9.
The interdependency of the molecular structures of drugs and their biomedical characteristics have already been proved by lab experiments. We can approximate these characteristics by computing numerical invariants associated to their molecular structures. These invariants are called topological indices. Among many topological indices, the face index (FI) is defined most recently. The FI may be helpful in approximating the boiling point and π-electron energy of benzenoid hydrocarbons and some other drugs with the correlation coefficient . In this article, we compute the FI for Boron triangular nanotubes, the nanotubes and , Also compute the FI for quadrilateral sections cut from regular hexagonal lattice and .
Sheng Ding; Muhammad Imran Qureshi; Syed Fehmeed Shah; Asfand Fahad; Muhammad Kamran Jamil; Jia‐Bao Liu. Face index of nanotubes and regular hexagonal lattices. International Journal of Quantum Chemistry 2021, 121, e26761 .
AMA StyleSheng Ding, Muhammad Imran Qureshi, Syed Fehmeed Shah, Asfand Fahad, Muhammad Kamran Jamil, Jia‐Bao Liu. Face index of nanotubes and regular hexagonal lattices. International Journal of Quantum Chemistry. 2021; 121 (19):e26761.
Chicago/Turabian StyleSheng Ding; Muhammad Imran Qureshi; Syed Fehmeed Shah; Asfand Fahad; Muhammad Kamran Jamil; Jia‐Bao Liu. 2021. "Face index of nanotubes and regular hexagonal lattices." International Journal of Quantum Chemistry 121, no. 19: e26761.
A graph’s entropy is a functional one, based on both the graph itself and the distribution of probability on its vertex set. In the theory of information, graph entropy has its origins. Dominating David derived networks have a variety of important applications in medication store, hardware, and system administration. In this study, we discuss dominating David derived network of type 1, 2, and 3 written as D 1 n , D 2 n , and D 3 n , respectively of order n . We also compute some degree-based entropies such as Randić , A B C , and GA entropy of D 1 n , D 2 n , and D 3 n .
Xuemei Zhao; Haidar Ali; Bilal Ali; Muhammad Ahsan Binyamin; Jia-Bao Liu; Ali Raza. Statistics and Calculation of Entropy of Dominating David Derived Networks. Complexity 2021, 2021, 1 -15.
AMA StyleXuemei Zhao, Haidar Ali, Bilal Ali, Muhammad Ahsan Binyamin, Jia-Bao Liu, Ali Raza. Statistics and Calculation of Entropy of Dominating David Derived Networks. Complexity. 2021; 2021 ():1-15.
Chicago/Turabian StyleXuemei Zhao; Haidar Ali; Bilal Ali; Muhammad Ahsan Binyamin; Jia-Bao Liu; Ali Raza. 2021. "Statistics and Calculation of Entropy of Dominating David Derived Networks." Complexity 2021, no. : 1-15.
In this paper, we give the relation between the spectrum of strongly regular graph and its clique-inserted graph. The Laplacian spectrum and the signless Laplacian spectrum of clique-inserted graph of strongly regular graph are calculated. We also give formulae expressing the energy, Kirchoff index, and the number of spanning trees of clique-inserted graph of a strongly regular graph. And, clique-inserted graph of the triangular graph T t , which is a strongly regular graph, is enumerated.
Chun-Li Kan; Ying-Ying Tan; Jia-Bao Liu; Bao-Hua Xing. Some Chemistry Indices of Clique-Inserted Graph of a Strongly Regular Graph. Complexity 2021, 2021, 1 -6.
AMA StyleChun-Li Kan, Ying-Ying Tan, Jia-Bao Liu, Bao-Hua Xing. Some Chemistry Indices of Clique-Inserted Graph of a Strongly Regular Graph. Complexity. 2021; 2021 ():1-6.
Chicago/Turabian StyleChun-Li Kan; Ying-Ying Tan; Jia-Bao Liu; Bao-Hua Xing. 2021. "Some Chemistry Indices of Clique-Inserted Graph of a Strongly Regular Graph." Complexity 2021, no. : 1-6.
Distance-based numeric parameters play a pivotal role in studying the structural aspects of networks which include connectivity, accessibility, centrality, clustering modularity, complexity, vulnerability, and robustness. Several tools like these also help to resolve the issues faced by the different branches of computer science and chemistry, namely, navigation, image processing, biometry, drug discovery, and similarities in chemical compounds. For this purpose, in this article, we are considering a family of networks that exhibits rotationally symmetric behaviour known as circular ladders consisting of triangular, quadrangular, and pentagonal faced ladders. We evaluate their upper bounds of fractional metric dimensions of the aforementioned networks.
Muhammad Javaid; Muhammad Kamran Aslam; Jia-Bao Liu. On the Upper Bounds of Fractional Metric Dimension of Symmetric Networks. Journal of Mathematics 2021, 2021, 1 -20.
AMA StyleMuhammad Javaid, Muhammad Kamran Aslam, Jia-Bao Liu. On the Upper Bounds of Fractional Metric Dimension of Symmetric Networks. Journal of Mathematics. 2021; 2021 ():1-20.
Chicago/Turabian StyleMuhammad Javaid; Muhammad Kamran Aslam; Jia-Bao Liu. 2021. "On the Upper Bounds of Fractional Metric Dimension of Symmetric Networks." Journal of Mathematics 2021, no. : 1-20.
This study provided a content analysis of studies aiming to disclose how artificial intelligence (AI) has been applied to the education sector and explore the potential research trends and challenges of AI in education. A total of 100 papers including 63 empirical papers (74 studies) and 37 analytic papers were selected from the education and educational research category of Social Sciences Citation Index database from 2010 to 2020. The content analysis showed that the research questions could be classified into development layer (classification, matching, recommendation, and deep learning), application layer (feedback, reasoning, and adaptive learning), and integration layer (affection computing, role-playing, immersive learning, and gamification). Moreover, four research trends, including Internet of Things, swarm intelligence, deep learning, and neuroscience, as well as an assessment of AI in education, were suggested for further investigation. However, we also proposed the challenges in education may be caused by AI with regard to inappropriate use of AI techniques, changing roles of teachers and students, as well as social and ethical issues. The results provide insights into an overview of the AI used for education domain, which helps to strengthen the theoretical foundation of AI in education and provides a promising channel for educators and AI engineers to carry out further collaborative research.
Xuesong Zhai; Xiaoyan Chu; Ching Sing Chai; Morris Siu Yung Jong; Andreja Istenic; Michael Spector; Jia-Bao Liu; Jing Yuan; Yan Li. A Review of Artificial Intelligence (AI) in Education from 2010 to 2020. Complexity 2021, 2021, 1 -18.
AMA StyleXuesong Zhai, Xiaoyan Chu, Ching Sing Chai, Morris Siu Yung Jong, Andreja Istenic, Michael Spector, Jia-Bao Liu, Jing Yuan, Yan Li. A Review of Artificial Intelligence (AI) in Education from 2010 to 2020. Complexity. 2021; 2021 ():1-18.
Chicago/Turabian StyleXuesong Zhai; Xiaoyan Chu; Ching Sing Chai; Morris Siu Yung Jong; Andreja Istenic; Michael Spector; Jia-Bao Liu; Jing Yuan; Yan Li. 2021. "A Review of Artificial Intelligence (AI) in Education from 2010 to 2020." Complexity 2021, no. : 1-18.
A graph’s entropy is a functional one, based on both the graph itself and the distribution of probability on its vertex set. In the theory of information, graph entropy has its origins. Hex-derived networks have a variety of important applications in medication store, hardware, and system administration. In this article, we discuss hex-derived network of type 1 and 2, written as HDN 1 n and HDN 2 n , respectively of order n . We also compute some degree-based entropies such as Randić, ABC , and G A entropy of HDN 1 n and HDN 2 n .
Pingping Song; Haidar Ali; Muhammad Ahsan Binyamin; Bilal Ali; Jia-Bao Liu. On Computation of Entropy of Hex-Derived Network. Complexity 2021, 2021, 1 -18.
AMA StylePingping Song, Haidar Ali, Muhammad Ahsan Binyamin, Bilal Ali, Jia-Bao Liu. On Computation of Entropy of Hex-Derived Network. Complexity. 2021; 2021 ():1-18.
Chicago/Turabian StylePingping Song; Haidar Ali; Muhammad Ahsan Binyamin; Bilal Ali; Jia-Bao Liu. 2021. "On Computation of Entropy of Hex-Derived Network." Complexity 2021, no. : 1-18.
Emergency logistics is not only a part of emergency management system, but also an important link of disaster relief and disaster reduction. The performance evaluation of emergency logistics capability is the foundation of improving emergency logistics capability. This paper took emergency logistics capability based on COVID-19 region as the research object. Firstly, we analyse the characteristics and influencing factors of public health emergency logistics. Secondly, we construct the evaluation system of public health emergency logistics capability. Thirdly, we establish the evaluation model of emergency logistics capability based on BP neural network. Finally, the evaluation model was applied to COVID-19 events, and the scientific nature and feasibility of the evaluation model were verified.
Yicheng Zhang; Qiying Ding; Jia-Bao Liu. Performance evaluation of emergency logistics capability for public health emergencies:perspective of COVID-19. International Journal of Logistics Research and Applications 2021, 1 -14.
AMA StyleYicheng Zhang, Qiying Ding, Jia-Bao Liu. Performance evaluation of emergency logistics capability for public health emergencies:perspective of COVID-19. International Journal of Logistics Research and Applications. 2021; ():1-14.
Chicago/Turabian StyleYicheng Zhang; Qiying Ding; Jia-Bao Liu. 2021. "Performance evaluation of emergency logistics capability for public health emergencies:perspective of COVID-19." International Journal of Logistics Research and Applications , no. : 1-14.
In this study, we first introduce polygonal cylinder and torus using Cartesian products and topologically identifications and then find their Wiener and hyper-Wiener indices using a quick, interesting technique of counting. Our suggested mathematical structures could be of potential interests in representation of computer networks and enhancing lattice hardware security.
Zhi-Ba Peng; Abdul Rauf Nizami; Zaffar Iqbal; Muhammad Mobeen Munir; Hafiz Muhammad Waqar Ahmed; Jia-Bao Liu. Wiener and Hyper-Wiener Indices of Polygonal Cylinder and Torus. Complexity 2021, 2021, 1 -15.
AMA StyleZhi-Ba Peng, Abdul Rauf Nizami, Zaffar Iqbal, Muhammad Mobeen Munir, Hafiz Muhammad Waqar Ahmed, Jia-Bao Liu. Wiener and Hyper-Wiener Indices of Polygonal Cylinder and Torus. Complexity. 2021; 2021 ():1-15.
Chicago/Turabian StyleZhi-Ba Peng; Abdul Rauf Nizami; Zaffar Iqbal; Muhammad Mobeen Munir; Hafiz Muhammad Waqar Ahmed; Jia-Bao Liu. 2021. "Wiener and Hyper-Wiener Indices of Polygonal Cylinder and Torus." Complexity 2021, no. : 1-15.
A complete classification of simple function germs with respect to Lipschitz equivalence over the field of complex numbers ℂ was given by Nguyen et al. The aim of this article is to implement a classifier in terms of easy computable invariants to compute the type of the Lipschitz simple function germs without computing the normal form in the computer algebra system Singular.
Yanan Liu; Muhammad Ahsan Binyamin; Adnan Aslam; Minahal Arshad; Chengmei Fan; Hassan Mahmood; Jia-Bao Liu. An Implementation of Lipschitz Simple Functions in Computer Algebra System Singular. Complexity 2021, 2021, 1 -5.
AMA StyleYanan Liu, Muhammad Ahsan Binyamin, Adnan Aslam, Minahal Arshad, Chengmei Fan, Hassan Mahmood, Jia-Bao Liu. An Implementation of Lipschitz Simple Functions in Computer Algebra System Singular. Complexity. 2021; 2021 ():1-5.
Chicago/Turabian StyleYanan Liu; Muhammad Ahsan Binyamin; Adnan Aslam; Minahal Arshad; Chengmei Fan; Hassan Mahmood; Jia-Bao Liu. 2021. "An Implementation of Lipschitz Simple Functions in Computer Algebra System Singular." Complexity 2021, no. : 1-5.
Topological index (TI) is a function that assigns a numeric value to a (molecular) graph that predicts its various physical and structural properties. In this paper, we study the sum graphs (S-sum, R-sum, Q-sum and T-sum) using the subdivision related operations and strong product of graphs which create hexagonal chains isomorphic to many chemical compounds. Mainly, the exact values of first general Zagreb index (FGZI) for four sum graphs are obtained. At the end, FGZI of the two particular families of sum graphs are also computed as applications of the main results. Moreover, the dominating role of the FGZI among these sum graphs is also shown using the numerical values and their graphical presentations.
Zhi-Ba Peng; Saira Javed; Muhammad Javaid; Jia-Bao Liu. Computing FGZ Index of Sum Graphs under Strong Product. Journal of Mathematics 2021, 2021, 1 -16.
AMA StyleZhi-Ba Peng, Saira Javed, Muhammad Javaid, Jia-Bao Liu. Computing FGZ Index of Sum Graphs under Strong Product. Journal of Mathematics. 2021; 2021 ():1-16.
Chicago/Turabian StyleZhi-Ba Peng; Saira Javed; Muhammad Javaid; Jia-Bao Liu. 2021. "Computing FGZ Index of Sum Graphs under Strong Product." Journal of Mathematics 2021, no. : 1-16.
A topological index is a numeric quantity assigned to a graph that characterizes the structure of a graph. Topological indices and physico-chemical properties such as atom-bond connectivity ABC , Randić, and geometric-arithmetic index GA are of great importance in the QSAR/QSPR analysis and are used to estimate the networks. In this area of research, graph theory has been found of considerable use. In this paper, the distinct degrees and degree sums of enhanced Mesh network, triangular Mesh network, star of silicate network, and rhenium trioxide lattice are listed. The edge partitions of these families of networks are tabled which depend on the sum of degrees of end vertices and the sum of the degree-based edges. Utilizing these edge partitions, the closed formulae for some degree-based topological indices of the networks are deduced.
Lei Ding; Syed Ahtsham Ul Haq Bokhary; Masood Ur Rehman; Usman Ali; Hirra Mubeen; Quaid Iqbal; Jia-Bao Liu. Degree-Based Indices of Some Complex Networks. Journal of Mathematics 2021, 2021, 1 -16.
AMA StyleLei Ding, Syed Ahtsham Ul Haq Bokhary, Masood Ur Rehman, Usman Ali, Hirra Mubeen, Quaid Iqbal, Jia-Bao Liu. Degree-Based Indices of Some Complex Networks. Journal of Mathematics. 2021; 2021 ():1-16.
Chicago/Turabian StyleLei Ding; Syed Ahtsham Ul Haq Bokhary; Masood Ur Rehman; Usman Ali; Hirra Mubeen; Quaid Iqbal; Jia-Bao Liu. 2021. "Degree-Based Indices of Some Complex Networks." Journal of Mathematics 2021, no. : 1-16.
Structure-based topological descriptors of chemical networks enable us the prediction of physico-chemical properties and the bioactivities of compounds through QSAR/QSPR methods. Topological indices are the numerical values to represent a graph which characterises the graph. One of the latest distance-based topological index is the Mostar index. In this paper, we study the Mostar index, Szeged index, PI index, ABC GG index, and NGG index, for chain oxide network COX n , chain silicate network CS n , ortho chain S n , and para chain Q n , for the first time. Moreover, analytically closed formulae for these structures are determined.
Min Hu; Haidar Ali; Muhammad Ahsan Binyamin; Bilal Ali; Jia-Bao Liu; Chengmei Fan. On Distance-Based Topological Descriptors of Chemical Interconnection Networks. Journal of Mathematics 2021, 2021, 1 -10.
AMA StyleMin Hu, Haidar Ali, Muhammad Ahsan Binyamin, Bilal Ali, Jia-Bao Liu, Chengmei Fan. On Distance-Based Topological Descriptors of Chemical Interconnection Networks. Journal of Mathematics. 2021; 2021 ():1-10.
Chicago/Turabian StyleMin Hu; Haidar Ali; Muhammad Ahsan Binyamin; Bilal Ali; Jia-Bao Liu; Chengmei Fan. 2021. "On Distance-Based Topological Descriptors of Chemical Interconnection Networks." Journal of Mathematics 2021, no. : 1-10.
Let G be a simple connected graph. Suppose Δ = Δ 1 , Δ 2 , … , Δ l an l -partition of V G . A partition representation of a vertex α w . r . t Δ is the l − vector d α , Δ 1 , d α , Δ 2 , … , d α , Δ l , denoted by r α | Δ . Any partition Δ is referred as resolving partition if ∀ α i ≠ α j ∈ V G such that r α i | Δ ≠ r α j | Δ . The smallest integer l is referred as the partition dimension pd G of G if the l -partition Δ is a resolving partition. In this article, we discuss the partition dimension of kayak paddle graph, cycle graph with chord, and a graph generated by chain of cycles. It has been shown that the partition dimension of the said families of graphs is constant.
Changcheng Wei; Muhammad Faisal Nadeem; Hafiz Muhammad Afzal Siddiqui; Muhammad Azeem; Jia-Bao Liu; Adnan Khalil. On Partition Dimension of Some Cycle-Related Graphs. Mathematical Problems in Engineering 2021, 2021, 1 -8.
AMA StyleChangcheng Wei, Muhammad Faisal Nadeem, Hafiz Muhammad Afzal Siddiqui, Muhammad Azeem, Jia-Bao Liu, Adnan Khalil. On Partition Dimension of Some Cycle-Related Graphs. Mathematical Problems in Engineering. 2021; 2021 ():1-8.
Chicago/Turabian StyleChangcheng Wei; Muhammad Faisal Nadeem; Hafiz Muhammad Afzal Siddiqui; Muhammad Azeem; Jia-Bao Liu; Adnan Khalil. 2021. "On Partition Dimension of Some Cycle-Related Graphs." Mathematical Problems in Engineering 2021, no. : 1-8.
A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. Wiener (1947) and Trinjastic and Gutman (1972) used molecular descriptors to find the boiling point of paraffin and total π -electron energy of the molecules, respectively. For molecular graphs, the general sum-connectivity and general Randić are well-studied fundamental topological indices (TIs) which are considered as degree-based molecular descriptors. In this paper, we obtain the bounds of the aforesaid TIs for the generalized F -sum graphs. The foresaid TIs are also obtained for some particular classes of the generalized F -sum graphs as the consequences of the obtained results. At the end, 3 D -graphical presentations are also included to illustrate the results for better understanding.
Jia Bao Liu; Sana Akram; Muhammad Javaid; Abdul Raheem; Roslan Hasni. Bounds of Degree-Based Molecular Descriptors for Generalized F -sum Graphs. Discrete Dynamics in Nature and Society 2021, 2021, 1 -17.
AMA StyleJia Bao Liu, Sana Akram, Muhammad Javaid, Abdul Raheem, Roslan Hasni. Bounds of Degree-Based Molecular Descriptors for Generalized F -sum Graphs. Discrete Dynamics in Nature and Society. 2021; 2021 ():1-17.
Chicago/Turabian StyleJia Bao Liu; Sana Akram; Muhammad Javaid; Abdul Raheem; Roslan Hasni. 2021. "Bounds of Degree-Based Molecular Descriptors for Generalized F -sum Graphs." Discrete Dynamics in Nature and Society 2021, no. : 1-17.
A numeric parameter which studies the behaviour, structural, toxicological, experimental, and physicochemical properties of chemical compounds under several graphs’ isomorphism is known as topological index. In 2018, Ali and Trinajstić studied the first Zagreb connection index Z C 1 to evaluate the value of a molecule. This concept was first studied by Gutman and Trinajstić in 1972 to find the solution of π -electron energy of alternant hydrocarbons. In this paper, the first Zagreb connection index and coindex are obtained in the form of exact formulae and upper bounds for the resultant graphs in terms of different indices of their factor graphs, where the resultant graphs are obtained by the product-related operations on graphs such as tensor product, strong product, symmetric difference, and disjunction. At the end, an analysis of the obtained results for the first Zagreb connection index and coindex on the aforesaid resultant graphs is interpreted with the help of numerical values and graphical depictions.
Muhammad Javaid; Usman Ali; Jia-Bao Liu. Computing Analysis for First Zagreb Connection Index and Coindex of Resultant Graphs. Mathematical Problems in Engineering 2021, 2021, 1 -19.
AMA StyleMuhammad Javaid, Usman Ali, Jia-Bao Liu. Computing Analysis for First Zagreb Connection Index and Coindex of Resultant Graphs. Mathematical Problems in Engineering. 2021; 2021 ():1-19.
Chicago/Turabian StyleMuhammad Javaid; Usman Ali; Jia-Bao Liu. 2021. "Computing Analysis for First Zagreb Connection Index and Coindex of Resultant Graphs." Mathematical Problems in Engineering 2021, no. : 1-19.
The entire world is struggling to control the spread of coronavirus (COVID‐19) as there are no proper drugs for treating the disease. Under clinical trials, some of the repurposed antiviral drugs have been applied to COVID‐19 patients and reported the efficacy of the drugs with the diverse inferences. Molecular topology has been developed in recent years as an influential approach for drug design and discovery in which molecules that are structurally related show similar pharmacological properties. It permits a purely mathematical description of the molecular structure so that in the development of identification of new drugs can be found through adequate topological indices. In this paper, we study the structural properties of the several antiviral drugs such as chloroquine, hydroxychloroquine, lopinavir, ritonavir, remdesivir, theaflavin, nafamostat, camostat, umifenovir and bevacizumab by considering the distance and bond measures of chemical compounds. Our quantitative values of the topological indices are extremely useful in the recent development of designing new drugs for COVID‐19.
Jia‐Bao Liu; Micheal Arockiaraj; M. Arulperumjothi; Savari Prabhu. Distance based and bond additive topological indices of certain repurposed antiviral drug compounds tested for treating COVID ‐19. International Journal of Quantum Chemistry 2021, 121, e26617 .
AMA StyleJia‐Bao Liu, Micheal Arockiaraj, M. Arulperumjothi, Savari Prabhu. Distance based and bond additive topological indices of certain repurposed antiviral drug compounds tested for treating COVID ‐19. International Journal of Quantum Chemistry. 2021; 121 (10):e26617.
Chicago/Turabian StyleJia‐Bao Liu; Micheal Arockiaraj; M. Arulperumjothi; Savari Prabhu. 2021. "Distance based and bond additive topological indices of certain repurposed antiviral drug compounds tested for treating COVID ‐19." International Journal of Quantum Chemistry 121, no. 10: e26617.