Weighted Mostar indices as measures of molecular peripheral shapes with applications to graphene, graphyne and graphdiyne nanoribbons

Self Cite

Szeged, PI and Mostar indices are some of the most investigated distance‐based molecular descriptors. Recently, many different variations of these topological indices appeared in the literature and sometimes they are all together called Szeged‐like topological indices. In this paper, we formally introduce the concept of a general Szeged‐like topological index, which includes all mentioned indices and also infinitely many other topological indices that can be defined in a similar way. As the main result of the paper, we provide a cut method for computing a general Szeged‐like topological index for any strength‐weighted graph. This greatly generalizes various methods known for some of the mentioned indices and therefore rounds off such investigations. Moreover, we provide applications of our main result to benzenoid systems, phenylenes, and coronoid systems, which are well‐known families of molecular graphs. In particular, closed‐form formulas for some subfamilies of these graphs are deduced.

“…Let G sw be a connected strength‐weighted graph and { E 1 , …, E k } be a c‐partition of E ( G ). Moreover, for i ∈ {1, …, k } let

G_{sw} / E_{i} = ((),,, G / E_{i}, {italicSW}_{v}^{i}, {italicSW}_{e}^{i})

be the strength‐weighted quotient graph, where the weights

w_{v}^{i}

s_{v}^{i}

w_{e}^{i}

, and

s_{e}^{i}

are defined as follows [31,37]:…”

Section: A General Cut Methodsmentioning

confidence: 99%

General cut method for computing Szeged‐like topological indices with applications to molecular graphs

Brezovnik

Tratnik

2020

Self Cite

“…Arockiaraj et al presented the results related to weighted Mostar indices of graphdiyne and some types of graphyne in ref. [28]. The Mostar index also appeared to be utilized in complex networks other than that in chemistry as the process of measurement of peripherality might also be utilized to find the different measures of centrality that dominate the research of these networks.…”

Section: Introductionmentioning

confidence: 99%

Mostar indices of SiO₂ nanostructures and melem chain nanostructures

Akhter

Imran

Iqbal

2020

Very recently, a bond‐additive topological invariant, known as the Mostar index, has been described as a measure of peripherality in networks and graphs. Since then, more versions of this index have been introduced and named the total Mostar index and the edge Mostar index. In this paper, we derive the Mostar indices of SiO2 nanostructures and C8 layer structures. Furthermore, we have also provided results related to the Mostar indices of melem chain nanostructures.

“…[18]. Arockiaraj et al [ 19 ] calculated the weighted Mostar indices of molecular peripheral shapes with applications in graphene, graphyne, and graphdiyne nanoribbons. Hayat and Zhou determined the extremal values of the Mostar index for the structures of trees and cacti in refs.…”

Section: Introductionmentioning

confidence: 99%

Edge Mostar index of chemical structures and nanostructures using graph operations

Imran

Akhter

Iqbal

2020

Recently, a new bond‐additive molecular topological descriptor, named the Mostar index, has been put forward as a measure of peripherality in chemical graphs and networks. In this article, we determine the edge versions of the Mostar index of a corona product, Cartesian product, join, Indu‐Bala product, and subdivision vertex‐edge join of graphs and implement these outcomes to find the edge Mostar index of several classes of chemical graphs and nanostructures.