The Edge Zagreb indices of Circumcoronene Series of Benzenoid

Abstract

In chemical graph theory, we have many invariant polynomials and topological indices for a molecular graph. One of the best known and widely used is the Zagreb topological index of a graph $G$ $M_1(G)$ introduced in 1972 by I. Gutman and N. Trinajstic and is defined as the sum of the squares of the degrees of all vertices of $G$, $M_{1}(G)=\sum\limits_{v\in V(G)} {d_{v}}^2$ (or $=\sum\limits_{e=uv\in E(G)} {d_{u}+d_{v}}$, where $d_{u}$ denotes the degree (number of first neighbors) of vertex $u$ in $G$. Also, the Second Zagreb index $M_2(G)$ is equal to $M_{2}(G)=\sum\limits_{e=uv\in E(G)} {d_{u} \times d_{v}}$. In this paper, we focus on the structure of molecular graph Circumcoronene Series of Benzenoid $H_{k}$ ($k>1$) and its line graph $L(H_{k})$ and counting First Zagreb index and Second Zagreb index of $L(H_{k})$.