University of KashanIranian Journal of Mathematical Chemistry2228-648911120200301Some New Results on Mostar Index of Graphs334210553810.22052/ijmc.2020.209321.1475ENModjtaba GhorbaniDepartment of mathematics, Shahid Rajaee Teacher Training University0000-0002-5324-0847Shaghayegh RahmaniDepartment of Mathematics, SRTT UniversityMohammad EslampoorDepartment of Mathematics, Srtt UniversityJournal Article20191125A general bond additive index (GBA) can be defined as , where α(e) is 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 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, compute the Mostar index of a family of nanocone graphs.https://ijmc.kashanu.ac.ir/article_105538_d4c7377f14f11fdb1555a6a0ed9f1700.pdf