The Generalized Zagreb Index of Capra-Designed Planar Benzenoid Series $Ca_k(C_6)$

et G = ( V , E ) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V ( G ) and E = E ( G ) , respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. In chemical graph theory, we have many topological indices for a molecular graph. The First and Second Zagreb indices are equal to M 1 ( G ) = ∑ u v ∈ E ( G ) [ d u + d v ] and M 2 ( G ) = ∑ u v ∈ E ( G ) d u d v , respectively. In this paper, we focus on the structure of Capra-designed planar benzenoid series C a k ( C 6 ) ( k ≥ 0 ) , and compute its Generalized Zagreb index.