F-index and hyper-Zagreb index of generalized middle graphs

Abstract

Graph invariants are numerical quantities connected with molecular graphs, and topological indices are one of them. Molecular descriptors are what they're called in mathematical chemistry. Quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies rely primarily on topological indices in mathematical chemistry. The F-index, or forgotten topological index, for a molecular graph G is equal to the sum of cubes of degrees of all vertices of the graph, while the hyper-Zagreb index is equal to the square of sum of degrees of all adjacent vertices of the graph. We obtain F-index, hyper-Zagreb index, and coindex values for generalised middle graphs G^xy and their complements of G^xy in this study.