Some New Results on Mostar Index of Graphs

A general bond additive index can be defined as GBA(Γ)=ƩeεE α(e), where α(e) is the edge contributions. The Mostar index is a new topological index whose edge contributions are α(e)=|nu - nv| in which nu is the number of vertices of Γ lying closer to vertex u than to vertex v and nv 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.