We were motivated to examine the quantitative structure–property relationships (QSPR) of nonsteroidal anti-inflammatory drugs (NSAIDs) by prior work on medicines. To do this, we made use of topological indices and analyzed the data (NSAIDs). A topological index is a measure that can be used to reflect the theoretical features of chemical substances. In this piece, well-known degree-based topological indices are applied to the chemical structures of medications that are used for the management of pain. These medicines include opiates, antidepressants, and others. These medications are taken to lessen or get rid of the feeling of discomfort in the affected area. When a molecule’s chemical structure is depicted as a graph, the elements themselves are considered to be the nodes of the graph, while the boundaries that exist between them take on the role of the graph’s edges. In addition, the QSPR analysis of topological indices was investigated, and the results showed that these indices have a strong correlation with the physical properties of chemical compounds that are used in the manufacturing of painkillers. This was demonstrated by the fact that topological indices were examined.

The shortest path algorithm is one of the best choices for implementation of data structures. The shortest path (SP) problem involves the problem of finding a suitable path between “two vertices or nodes in a graph” in such a way that the sum of the weights of its component edges is minimal. There are many theories for solving this problem one of the widely used way solution for solving this problem is Dijkstra’s algorithm (DA) which is also widely used in many engineering calculation works also. There are two types of DA one is the basic one and other one is optimized. This paper is focused on the basics one which provides a shortest route between source node and the destination node. Main focus has been kept on keeping the work simple and easy to understand with some basic concepts .Storage space and operational efficiency improvement has been tried to improve.

Rough set theory is a method of information processing for database systems. The neutrosophic matrix is a generalization of the fuzzy matrix, especially in handling indeterminacy situations. The concept of matrix theory and its energy in the neutrosophic environment help to determine the value of the uncertain matrix. In this paper, we correlate the rough set theory with the neutrosophic matrix theory to introduce the rough neutrosophic matrix (RNM). In this structure, lower and upper approximation neutrosophic matrices are used to deal with uncertain situations. We demonstrate that the given matrix plays a different role in decision-making situations and defined the proposed matrix's determinant, adjoint, algebraic properties and operations. Finally, derived the ranking function for a rough neutrosophic matrix's energy. The new multi-criteria decision-making (MCDM) approach was presented with the ranking formula, which was utilized to rank the alternatives, and numerical examples were provided to show how the proposed matrix and its energy could be applied to an MCDM problem.

In this review article, we have discussed about energy of a graph and energy of a fuzzy graph. Further we presented some standard results on these graphs. Since most real world networks such as communication networks, data organization, computational devices, the flow of computation, web graphs etc are directed graphs, we have analyzed energy of an intuitionistic fuzzy directed graph through real time example.

Contents IJPAM: Volume 98, No. 3 (2015)