Graph invariants based on distance between edges and double graphs

Abstract

Topological indices are numerical parameters of graph which characterize its topology and are invariant under graph isomorphism. They are applied in theoretical chemistry for the design of chemical compounds with certain physicochemical properties or biological activities. The Wiener index, hyper-Wiener index, degree distance, and Gutman index are among the best-known distance-based topological indices with known applications in chemistry. In this paper, we study the edge version of these graph invariants for a collection of graphs named double graphs.