Mostar index: Results and perspectives

作者：

Highlights：

• The Mostar index is a recently introduced bond-additive distance-based graph invariant that measures the degree of peripherality of particular edges and of the graph as a whole.

• This paper aims to gather some known bounds and extremal results concerning the Mostar index. Also, it presents various modifications and generalizations of the aforementioned index and it outlines several possible directions of further research.

• Finally, some open problems and conjectures are listed.

摘要

•The Mostar index is a recently introduced bond-additive distance-based graph invariant that measures the degree of peripherality of particular edges and of the graph as a whole.•This paper aims to gather some known bounds and extremal results concerning the Mostar index. Also, it presents various modifications and generalizations of the aforementioned index and it outlines several possible directions of further research.•Finally, some open problems and conjectures are listed.

论文关键词：Chemical graph theory,Topological indices,Distance in graphs,Mostar index,Extremal problems in graph theory,Topological coindex,Graph polynomial,Graph spectra,Graph invariants,Meixner polynomial

论文评审过程：Received 14 December 2020, Revised 25 March 2021, Accepted 27 March 2021, Available online 13 April 2021, Version of Record 13 April 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126245