On cacti with large Mostar index

Abstract

The Mostar index of a graph G is defined as the sum of absolute values of the differences between n u and n v over all edges e = uv of G, where n u (e) and n v (e) are respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we determine all the n-vertex cacti with the largest Mostar index, and we give a sharp upper bound of the Mostar index for cacti of order n with k cycles, and characterize all the cacti that achieve this bound.

On Distance-Based Topological Descriptors of Chemical Interconnection Networks

“…A topological index, specially, the Mostar index is one of the latest topological index, derived in 2018 [13]. Previously, Arockiaraj [14] found the Mostar indices of carbon nanostructures, and Hayata and Zhou [15] calculated the large Mostar index on cacti. e Mostar index for a graph G is defined as the sum of all the absolutes values of the difference between n u and n v , where u and v are the adjacent vertices of an edge:…”

Mostar indices of SiO2 nanostructures and melem chain nanostructures

“…[23]. Hayat and Zhou gave the expressions of this index for the cacti and trees in refs [24,25]. Recently, by using graph operations, Mostar indices of nanostructures and chemical structures have been computed in ref.…”

The Topological Aspects of Phthalocyanines and Porphyrins Dendrimers

“…For further results related to different version of Mostar index, the interested readers is refereed to [26], [27], [29], [30], [32]- [34]. The evaluation and analysis of topological indices of molecular structures are modern trends of research, which are of the significant importance in nanotechnology and theoretical chemistry.…”