Dr. Bilal Ahmad Ahmad Rather
United Arab Emirates University, Al Ain, United Arab Emirates
'%3e%3cpath%20d='M22.1642%2019.0924C21.7317%2018.068%2021.1041%2017.1375%2020.3163%2016.3527C19.5309%2015.5656%2018.6006%2014.9381%2017.5766%2014.5048C17.5674%2014.5002%2017.5582%2014.4979%2017.5491%2014.4933C18.9774%2013.4616%2019.9059%2011.7811%2019.9059%209.88504C19.9059%206.74408%2017.3611%204.19922%2014.2201%204.19922C11.0792%204.19922%208.53429%206.74408%208.53429%209.88504C8.53429%2011.7811%209.46282%2013.4616%2010.8912%2014.4956C10.882%2014.5002%2010.8728%2014.5025%2010.8636%2014.5071C9.83652%2014.9404%208.91487%2015.5617%208.1239%2016.355C7.33685%2017.1404%206.70933%2018.0707%206.276%2019.0947C5.85031%2020.0972%205.62072%2021.172%205.59967%2022.2609C5.59905%2022.2853%205.60335%2022.3097%205.61229%2022.3325C5.62123%2022.3553%205.63465%2022.376%205.65174%2022.3935C5.66883%2022.4111%205.68926%2022.425%205.71182%2022.4345C5.73437%2022.444%205.7586%2022.4489%205.78308%2022.4489H7.15868C7.25956%2022.4489%207.3398%2022.3686%207.3421%2022.2701C7.38795%2020.5001%208.09868%2018.8425%209.35506%2017.5861C10.655%2016.2862%2012.3814%2015.5709%2014.2201%2015.5709C16.0588%2015.5709%2017.7852%2016.2862%2019.0852%2017.5861C20.3415%2018.8425%2021.0523%2020.5001%2021.0981%2022.2701C21.1004%2022.3709%2021.1807%2022.4489%2021.2815%2022.4489H22.6571C22.6816%2022.4489%2022.7058%2022.444%2022.7284%2022.4345C22.751%2022.425%2022.7714%2022.4111%2022.7885%2022.3935C22.8056%2022.376%2022.819%2022.3553%2022.8279%2022.3325C22.8369%2022.3097%2022.8412%2022.2853%2022.8406%2022.2609C22.8176%2021.165%2022.5907%2020.0989%2022.1642%2019.0924ZM14.2201%2013.8284C13.1678%2013.8284%2012.1773%2013.418%2011.4322%2012.6729C10.6871%2011.9278%2010.2767%2010.9374%2010.2767%209.88504C10.2767%208.83271%2010.6871%207.84227%2011.4322%207.09715C12.1773%206.35204%2013.1678%205.94165%2014.2201%205.94165C15.2724%205.94165%2016.2629%206.35204%2017.008%207.09715C17.7531%207.84227%2018.1635%208.83271%2018.1635%209.88504C18.1635%2010.9374%2017.7531%2011.9278%2017.008%2012.6729C16.2629%2013.418%2015.2724%2013.8284%2014.2201%2013.8284Z'%20fill='%238590A2'/%3e%3c/g%3e%3c/svg%3e)
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Academic Career Length
7Years (2020-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
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Journal Article
Bilal Ahmad Ahmad Rather
Shariefuddin PirzadaTNTariq A. Naikoo
Tariq A. Naikoo
Yilun ShangGiven a commutative ring R with identity , let the set denote the set of zero-divisors and let be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by , is a simple graph whose vertex set is and each pair of vertices in are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs for , where are primes and are positive integers.
1 April 2022 in Match Communications in Mathematical and in Computer Chemistry
Journal Article
Bilal Ahmad Ahmad Rather
Muhammad Imran25 October 2020 in Linear and Multilinear Algebra
Journal Article
Shariefuddin PirzadaBilal Ahmad Ahmad RatherMAM. Aijaz
M. Aijaz
TCT. A. Chishti
T. A. Chishti
For a simple connected graph G of order n, we obtain the distance signless Laplacian spectrum of the joined union of regular graphs in terms of their adjacency spectrum and the spectrum of an auxiliary matrix. As a consequence, we obtain the distance signless Laplacian spectrum of the zero divisor graphs of finite commutative rings for some values of n. We show that is not in general distance signless Laplacian integral for , where p is any prime and Also, we find the spectrum of for certain values of z.
Journal Article
FAFawad Ali
Fawad AliBilal Ahmad Ahmad RatherNFNahid Fatima
Nahid Fatima
Muhammad Sarfraz
Asad UllahRDRahim Dad
Rahim Dad +1
A topological index is a number generated from a molecular structure (i.e., a graph) that indicates the essential structural properties of the proposed molecule. Indeed, it is an algebraic quantity connected with the chemical structure that correlates it with various physical characteristics. It is possible to determine several different properties, such as chemical activity, thermodynamic properties, physicochemical activity, and biological activity, using several topological indices, such as the geometric-arithmetic index, arithmetic-geometric index, Randić index, and the atom-bond connectivity indices. Consider as a group and H as a non-empty subset of . The commuting graph , has H as the vertex set, where are edge connected whenever and commute in . This article examines the topological characteristics of commuting graphs having an algebraic structure by computing their atomic-bond connectivity index, the Wiener index and its reciprocal, the harmonic index, geometric-arithmetic index, Randić index, Harary index, and the Schultz molecular topological index. Moreover, we study the Hosoya properties, such as the Hosoya polynomial and the reciprocal statuses of the Hosoya polynomial of the commuting graphs of finite subgroups of . Finally, we compute the Z-index of the commuting graphs of the binary dihedral groups.
16 October 2021 in Electronic Journal of Graph Theory and Applications
Journal Article
SPS. Pirzada
S. Pirzada
Bilal Ahmad Ahmad RatherTCT. A. Chishti
T. A. Chishti
USU. Samee
U. Samee
On normalized Laplacian spectrum of zero divisor graphs of commutative ring ℤn
29 March 2021 in Carpathian Mathematical Publications
Journal Article
For a finite commutative ring $\mathbb{Z}_{n}$ with identity $1\neq 0$, the zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $x$ and $y$ are adjacent if and only if $xy=0$. We find the distance Laplacian spectrum of the zero divisor graphs $\Gamma(\mathbb{Z}_{n})$ for different values of $n$. Also, we obtain the distance Laplacian spectrum of $\Gamma(\mathbb{Z}_{n})$ for $n=p^z$, $z\geq 2$, in terms of the Laplacian spectrum. As a consequence, we determine those $n$ for which zero divisor graph $\Gamma(\mathbb{Z}_{n})$ is distance Laplacian integral.
About Me
Bilal Ahmad Rather was born and raised in Srinagar, Kashmir. He earned master's degree in mathematics and diploma in computer applications (including BSc, B.ed, SET2018) from University of Kashmir, J&K, India. From August 2017 to June 2019, he was employed as a junior research fellow on a major research project funded by SERB-DST (EMR/2015/0010471). In February 2021, he earned his doctorate in mathematics and his thesis, "On distribution of Laplacian eigenvalues of graphs", was nominated by the Dr. K. V. Rao Scientific Society (KVRSS), Hyderabad, India, for the 2021 Annual Research Awards. From February to March 2021, he served as a guest lecturer at the JK Institute of Mathematical Sciences. He worked as a postdoctoral fellow from May 2021-May 2024 at the United Arab Emirates University in the United Arab Emirates. From June 2024 to present date, he is working as postdoc associate at SDUT China. His main research interests include combinatorial matrix theory, combinatorial commutative algebra, and their applications in theoretical computer science and mathematical chemistry. He has published more than 70 Sci papers and his works have appeared in a number of reputable journals, including Linear Algebra and its Applications, Electronic Journal of Linear Algebra, Journal of Algebra and its Applications, Communication in Algebra, Discrete Applied Mathematics, Linear and Multilinear Algebra, Applied Mathematics and Computations, Special Matrices and several others.
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