The Generalized Zagreb Index of Capra-Designed Planar Benzenoid Series [latex]Ca_k(C_6)[/latex]

• Main Authors: Muhammad S. Sardar, Sohail Zafar, Mohammad R. Farahani
• Format: Article
• Language: English
• Published: Ptolemy Scientific Research Press 2017-09-01
• Series: Open Journal of Mathematical Sciences
• Subjects: Molecular Graph; Capra Operation; Benzenoid Series; Generalized Zagreb Index.
• Online Access: https://openmathscience.com/the-generalized-zagreb-index-of-capra-designed-planar-benzenoid-series/

Let [latex]G=(V,E)[/latex] be a simple connected graph. The sets of vertices and edges of [latex]G[/latex] are denoted by [latex]V=V(G)[/latex] and [latex]E=E(G)[/latex], 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 [latex]M_1(G)=\sum_{uv \in E(G)}[d_u+d_v][/latex] and [latex]M_2(G)=\sum_{uv \in E(G)} d_{u}d_{v}[/latex], respectively. In this paper, we focus on the structure of Capra-designed planar benzenoid series [latex]Ca_k(C_6)[/latex] [latex](k\geq0)[/latex], and compute its Generalized Zagreb index.