On the extremal values for the Mostar index of trees with given degree sequence

Deng, Kecai; Li, Shuchao

doi:10.1016/j.amc.2020.125598

Cited by 13 publications

(8 citation statements)

References 11 publications

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“…These quantities are some of the central and most commonly studied distance-based topological descriptors. For example, see recent research on Szeged indices [12][13][14][15], Mostar indices [16][17][18][19],…”

Section: Introductionmentioning

confidence: 99%

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

Brezovnik

Tratnik

2020

Int J of Quantum Chemistry

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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.

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Section: Introductionmentioning

confidence: 99%

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

Brezovnik

Tratnik

2020

Int J of Quantum Chemistry

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“…Deng and Li [7] investigated extremal bounds for the Mostar index of trees with a given order and degree sequence, as well as trees with a given order and independence number. Ghorbani et al [14] proved a lower bound of 2∆(n − 3) on the Mostar index of any tree of order n ≥ 3 and maximum degree ∆.…”

Section: − O(n)mentioning

confidence: 99%

Peripherality in networks: theory and applications

Geneson¹,

Tsai²

2021

Preprint

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We investigate several related measures of peripherality and centrality for vertices and edges in networks, including the Mostar index which was recently introduced as a measure of peripherality for both edges and networks. We refute a conjecture on the maximum possible Mostar index of bipartite graphs from (Došlić et al, Journal of Mathematical Chemistry, 2018) and(Ali and Došlić, Applied Mathematics and Computation, 2021). We also correct a result from the latter paper, where they claimed that the maximum possible value of the terminal Mostar index among all trees of order n is (n − 1)(n − 2). We show that this maximum is (n − 1)(n − 3) for n ≥ 3, and that it is only attained by the star.We asymptotically answer another problem on the maximum difference between the Mostar index and the irregularity of trees from (F. Gao et al, On the difference of Mostar index and irregularity of graphs, Bulletin of the Malaysian Mathematical Sciences Society, 2021). We also prove a number of extremal bounds and computational complexity results about the Mostar index, irregularity, and measures of peripherality and centrality.We discuss graphs where the Mostar index is not an accurate measure of peripherality. We construct a general family of graphs with the property that the Mostar index is strictly greater for edges that are closer to the center. We also investigate centrality and peripherality in two graphs which represent the SuperFast and MOZART-4 systems of atmospheric chemical reactions by computing various measures of peripherality and centrality for the vertices and edges in these graphs. For both of these graphs, we find that the Mostar index is closer to a measure of centrality than peripherality of the edges. We also introduce some new indices which perform well as measures of peripherality on the SuperFast and MOZART-4 graphs.

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“…N. Dehgardiy and M. Azariz obtained the lower bounds with the Mostar index of trees and the Mostar index of some graph operations [8]. K. Deng and S. Li presented the extremal values for the Mostar index of trees with given degree sequence [9]. K. Deng and S. Li studied the Mostar index for Chemical trees [10].…”

Section: Introductionmentioning

confidence: 99%

“…K. Deng and S. Li presented the extremal values for the Mostar index of trees with given degree sequence [9]. K. Deng and S. Li studied the Mostar index for Chemical trees [10]. Ö. Colakoglu Havare gave the value of the Mostar index and edge Mostar index for some cycle-related graphs [6].…”

Section: Introductionmentioning

confidence: 99%

Some inequalities on the Mostar index

HAVARE¹

2022

CMI

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"Topological indices are the numerical descriptors of a molecular structure obtained via molecular graph G. They are used to predict physicochemical and bioactive properties of the molecules and molecular compounds. In this paper, the Mostar index is studied. It is presented the relationships between the Mostar index and other topological indices. Inequalities about some parameters and also Nordhaus-Gaddum-type results for the Mostar index are also presented."

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On the extremal values for the Mostar index of trees with given degree sequence

Cited by 13 publications

References 11 publications

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

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

Peripherality in networks: theory and applications

Some inequalities on the Mostar index

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