Sombor index and degree-related properties of simplicial networks

Shang, Yilun

doi:10.1016/j.amc.2021.126881

Cited by 55 publications

(21 citation statements)

References 45 publications

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“…Successful predictive potential of the Sombor index has also been employed for simulating the thermodynamic characteristics of organic compounds. The reader is referred to [1][2][3][4][5][6][7][8][9][10][11]13,[16][17][18][19][20][21][22][23][24]26,27,30], for a detailed mathematical treatment of the Sombor index of graphs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Sombor Index of Graphs with a Given Number of Cut-Vertices

Hayat¹,

Rehman²

2022

MATCH

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Introduced by Gutman in 2021, the Sombor index is a novel graph-theoretic topological descriptor possessing potential applications in the modeling of thermodynamic properties of compounds. Let H k n be the family of graphs on order n and k number of cutvertices having at least one cycle. In this paper, we present minimum Sombor indices of graphs in H k n. The corresponding extremal graphs have been characterized as well.

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Section: Introductionmentioning

confidence: 99%

“…After its chemical applicability was reported, the Sombor index has been studied by mathematicians as well as theoretical chemists. Various mathematical properties of the Sombor index have been reported, for instance, in [2,4,6,7,8,9,10,11,12,14,16,17,18,22,24,25,26,27,29,30,31,32,33,35,36,42,44].…”

Section: Introductionmentioning

confidence: 99%

On Sombor Index of Graphs with a Given Number of Cut-Vertices

Hayat¹,

Rehman²

2022

MATCH

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“…In recent years, graph operations have attracted extensive attention of scholars. Y. Shang used the edge corona product to construct a simplicial network and, based on the degree of network vertices, studied the recently widely concerned Sombor index [11]. J. Liu presented a kind of weighted edge corona networks and obtained the Laplacian and signless Laplacian spectra of the weighted edge corona networks, and a specific application example is given by calculating the number of spanning trees and the Kirchhoff index [12].…”

Section: Introductionmentioning

confidence: 99%

Consensus analysis of the weighted corona networks

Zhu

Gao³

et al. 2022

Front. Phys.

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The consensus of complex networks has attracted the attention of many scholars. The graph operation is a common method to construct complex networks, which is helpful in studying the consensus of complex networks. Based on the corona networks G1◦G2, this study gives different weights to the edges of G1◦G2 to obtain the weighted corona networks G̃1◦G̃2 and studies the consensus of G̃1◦G̃2. The consensus of the networks can be measured by coherence. First, the Laplacian polynomial of G̃1◦G̃2 is derived by using the properties of an orthogonal matrix. Second, the relationship between the first-order coherence of G̃1◦G̃2 and G1 is deduced by using the relevant properties of the determinant and the conclusion of polynomial coefficients and the principal minors of the matrix. Third, the join operation is introduced to further simplify the analytical formula of network coherence. Finally, a specific network example is used to verify the validity of the conclusion.

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“…Successful predictive potential of the Sombor index has also been employed for simulating the thermodynamic characteristics of organic compounds. The reader is referred to [1,2,3,4,5,6,7,8,9,10,11,13,16,17,18,19,20,21,22,23,24,26,27,30], for a detailed mathematical treatment of the Sombor index of graphs.…”

Section: Introductionmentioning

confidence: 99%

On Sombor index of graphs with a given number of cut-vertices

Hayat¹,

Rehman²,

Zhong³

2022

Preprint

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Introduced by Gutman in 2021, the Sombor index is a novel graph-theoretic topological descriptor possessing potential applications in the modeling of thermodynamic properties of compounds. Let G k n be the set of all n-vertex connected graphs with k cut-vertices. In this paper, we present minimum Sombor indices of graphs in G k n . The corresponding extremal graphs have been characterized as well.

show abstract

Sombor index and degree-related properties of simplicial networks

Cited by 55 publications

References 45 publications

On Sombor Index of Graphs with a Given Number of Cut-Vertices

On Sombor Index of Graphs with a Given Number of Cut-Vertices

Consensus analysis of the weighted corona networks

On Sombor index of graphs with a given number of cut-vertices

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