On topological properties of some convex polytopes by using line operator on their subdivisions

Abstract

In this paper, we give theoretical results for some topological indices such as Zagreb indices $M_{1}(G)$, $M_{2}(G)$, $M_{3}(G)$, $R(G)$, $M_{1}(\overline{G})$, $M_{2}(\overline{G})$, Zagreb coindices $\overline{M_{1}}(G)$, $\overline{M_{2}}(G)$, $\overline{M_{2}}(\overline{G})$ hyper-Zagreb index $HM(G)$,atom-bond connectivity index $ABC(G)$, sum connectivity index $\chi(G)$ and geometric-arithmetic connectivity index $GA(G)$, by considering $G$ as line graph of subdivision of some convex polytopes and $\overline{G}$ denotes its complement.