First General Zagreb Co‐Index of Graphs under Operations

Abstract

Topological indices are graph-theoretic parameters which are widely used in the subject of chemistry and computer science to predict the various chemical and structural properties of the graphs respectively. Let G be a graph; then, by performing subdivision-related operations S , Q , R , and T on G , the four new graphs S G (subdivision graph), Q G (edge-semitotal), R G (vertex-semitotal), and T G (total graph) are obtained, respectively. Furthermore, for two simple connected graphs G and H , we define F -sum graphs (denoted by G + F H ) which are obtained by Cartesian product of F G and H , where F ∈ S , R , Q , T . In this study, we determine first general Zagreb co-index of graphs under operations in the form of Zagreb indices and co-indices of their basic graphs.