Some New Results on Mostar Index of Graphs

A general bond additive index can be defined as GBA(Gamma) = Sigma(e is an element of E) alpha(e), where alpha(e) is the edge contributions. The Mostar index is a new topological index whose edge contributions are alpha(e)=vertical bar n(u) - n(v)vertical bar in which n(u) is the number of vertices of Gamma lying closer to vertex u than to vertex v and n(v) can be defined similarly. In this paper, we propose some new results on the Mostar index based on the vertex-orbits under the action of automorphism group. In addition, we detrmined the structures of graphs with Mostar index equal 1. Finally, we compute the Mostar index of a family of nanocone graphs. (C) 2020 University of Kashan Press. All rights reserved