Extremal bicyclic graphs with respect to Mostar index

Abstract

For an edge uv of a graph G, nu denotes the number of vertices of G closer to u than to v, and similarly nv is the number of vertices closer to v than to u. The Mostar index of a graph G is defined as the sum of absolute differences between nu and nv over all edges uv of G. In the paper we prove a recent conjecture of Došlić et al. (2018) on a characterization of bicyclic graphs with given number of vertices, for which extremal values of Mostar index are attained.