The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

Fang, Xiaona; You, Lihua; Liu, Hechao

doi:10.48550/arxiv.2103.07172

Cited by 3 publications

(4 citation statements)

References 19 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%

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

Hayat¹,

Rehman²

2022

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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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“…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.

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“…Even though Sombor indices were introduced very recently, there are already several works available in the literature where these indices are applied to chemical graphs of interest, see e.g. [4,5,[7][8][9][10][11][12][13][14][15][16][17][18]. Also, bounds for Sombor indices as well as relations among them and with many other topological indices have been reported in [4,10,[19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Normalized Sombor indices as complexity measures of random graphs

Aguilar-Sanchez,

Mendez-Bermudez,

Rodriguez

et al. 2021

Preprint

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We perform a detailed computational study of the recently introduced Sombor indices on random graphs. Specifically, we apply Sombor indices on three models of random graphs: Erdös-Rényi graphs, random geometric graphs, and bipartite random graphs. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the graph, scale with the graph average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random graphs and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the graph adjacency matrix.

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The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs

Cited by 3 publications

References 19 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

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

Normalized Sombor indices as complexity measures of random graphs

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