Edge Mostar Indices of Cacti Graph With Fixed Cycles

Yasmeen, Farhana; Akhter, Shehnaz; Ali, Kashif; Rizvi, Syed T. R.

doi:10.3389/fchem.2021.693885

Cited by 6 publications

(2 citation statements)

References 31 publications

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“…Theorem 1. [34] Let Ω ∈ C(n, k) be a connected graph. Then The second maximum edge Mostar index for C(n, k) with the following given conditions determined by Liu et al [24].…”

Section: Preliminaries Results and Notationsmentioning

confidence: 99%

On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter

Asmat,

Askar

et al. 2023

Eur. J. Pure Appl. Math.

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It was introduced by Doˇsli ́c and Ivica et al. (Journal of Mathematical chemistry, 56(10) (2018): 2995–3013), as an innovative graph-theoretic topological identifier, the Mostar index is significant in simulating compounds’ thermodynamic properties in simulations, which is defined as sum of absolute values of the differences among nu(e|Ω) and nv(e|Ω) over all lines e = uv ∈ Ω, where nu(e|Ω) (resp. nv(e|Ω)) is the collection of vertices of Ω closer to vertex u (resp. v) than to vertex v (resp. u). Let C(n, k) be the set of all n-vertex cacti graphs with exactly k cycles and T(n, d) be the set of all n-vertex tree graphs with diameter d. It is said that a cacti is a connected graph with blocks that comprise of either cycles or edges. Beginning with the weighted Mostar index of graphs, we developed certain transformations that either increase or decrease index. To advance this analysis, we determine the extreme graphs where the maximum and minimum values of the weighted edge Mostar index are accomplished. Moreover, we compute the maximum weighted vertex Mostar invariant for trees with order n and fixed diameter d.

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“…Theorem 1. [34] Let Ω ∈ C(n, k) be a connected graph. Then The second maximum edge Mostar index for C(n, k) with the following given conditions determined by Liu et al [24].…”

Section: Preliminaries Results and Notationsmentioning

confidence: 99%

On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter

Asmat,

Askar

et al. 2023

Eur. J. Pure Appl. Math.

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show abstract

“…Example, for a path P 3 of length 3, denote its four vertices as With respect to the edge Mostar index, the extremal graphs among polymers [14], trees and unicyclic graphs [15], cacti graphs with fixed cycles [16], cycle-related graphs [17], and the minimum values of bicyclic graphs [18], have been studied.…”

Section: Introductionmentioning

confidence: 99%

The Upper Bound of the Edge Mostar Index with Respect to Bicyclic Graphs

Wang

Liu

2023

Mathematics

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Let G be a connected graph; the edge Mostar index Moe(G) of G is defined as Moe(G)=∑e=uv∈E(G)|mu(e)−mv(e)|, where mu(e) and mv(e) denote the number of edges in G that are closer to vertex u than to vertex v and the number of edges that are closer to vertex v than to vertex u, respectively. In this paper, we determine the upper bound of the edge Mostar index for all bicyclic graphs and identify the extremal graphs that achieve this bound.

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Cyclic connectivity index of bipolar fuzzy incidence graph

Zhu

Gao

2022

Open Chemistry

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In the performance characterization of chemical molecular structures, several uncertain properties are often encountered, and fuzzy theory is precisely the tool to characterize these uncertainties. When molecular structures are described by molecular graphs, the corresponding fuzzy graph theory is used to characterize the uncertainty of atoms and atomic bonds. In this study, there is introduced cyclic connectivity index and its average version for bipolar fuzzy incidence graph (BFIG), and several theoretical results are obtained in the light of graph theory and fuzzy theory. Finally, the given new fuzzy index is applied to the testing of anti-aging-related drugs yields average uncertainty data for the corresponding molecular structures.

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Edge Mostar Indices of Cacti Graph With Fixed Cycles

Cited by 6 publications

References 31 publications

On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter

On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter

The Upper Bound of the Edge Mostar Index with Respect to Bicyclic Graphs

Cyclic connectivity index of bipolar fuzzy incidence graph

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