Comparison between Szeged indices of graphs

Abstract

The Szeged index Sz(G) of a simple connected graph G is the sum of the terms n_u(e)n_v (e) over all edges e = uv of G, where n_u(e) is the number of vertices of G lying closer to u than v, and n_v (e) is defined analogously. The aim of this paper is to present some relationship between Szeged index and some of its variants such as the edge-vertex Szeged index, the vertex-edge Szeged index and revised Szeged index. Moreover, we obtain lower and upper bounds on the difference between vertex-edge Szeged index and edge-vertex Szeged index of unicyclic graphs.