Mostar index: Results and perspectives

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. It attracted considerable attention, both in the context of complex networks and in more classical applications of chemical graph theory, where it turned out to be useful as a measure of the total surface area of octane isomers and as a tool for studying topological aspects of fullerene shapes. 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. (c) 2021 Elsevier Inc. All rights reserved.