Neighborhood M-Polynomial of Graph Operations: Exploring Nanostructure Applications and Correcting Cycle-Related Graph Results
نویسندگان
1 Department of Mathematics, NEHU, Shillong, India
2 Department of Mathematics, NEHU, Shillong, India
3 Mathematics Division, Department of Basic Sciences and Social Sciences, NEHU, Shillong, India
doi
10.22052/ijmc.2024.253190.1733چکیده
Mathematical chemistry is a field of mathematics where chemical compounds are studied by associating a graph to it. A topological index serves as a mathematical invariant that elucidates the underlying topological arrangement of molecules or networks. This paper explores the neighborhood M-Polynomial concerning various graph operations of regular graphs. Additionally, it addresses and rectifies several erroneous results pertaining to cycle-related graphs that were previously reported. Furthermore, we examine the applications of the neighborhood $M$-Polynomial to the $VPHX[m,n]$ nanotubes and $VPHY[m,n]$ nanotori, presenting their potential in real-world. Through this comprehensive investigation, we aim to advance the understanding of topological indices and their practical implications.