First General Zagreb Co‐Index of Graphs under Operations

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.