Complementary Topological Indices

Abstract

An edge of a graph can be geometrically represented by points (dr, ds) and (ds, dr) in a 2D coordinate system, where coordinates are, obviously, the degrees of the edge’s end-vertices. Recently, using such a geometrical point of view of a graph edge, a couple of topological invariants were put forward. They have attracted considerable attention among chemical graph theorists. This paper introduces a novel approach for devising “geometrical” topological indices. Finally, special attention is focused on the complementary second Zagreb index as a representative of the introduced approach.