Ordering chemical graphs by Sombor indices and its applications

Liu, Hechao; You, Lihua; Huang, Yufei

doi:10.46793/match.87-1.005l

Cited by 49 publications

(30 citation statements)

References 10 publications

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“…5(e,f), the curves of the main panels are now properly scaled when plotted as a function of p. k = np/2, we get exactly the same expressions listed in Eqs. (13)(14)(15)(16)(17). This is verified in Figs.…”

Section: Sombor Indices On Bipartite Random Graphssupporting

confidence: 72%

“…Moreover, the applicability of Eqs. (13)(14)(15)(16)(17) to the three random graph models we study here allow us to relate the average value of a…”

Section: General Scaling Of Sombor Indices On Random Graphsmentioning

confidence: 99%

“…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%

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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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Section: Sombor Indices On Bipartite Random Graphssupporting

confidence: 72%

“…Moreover, the applicability of Eqs. (13)(14)(15)(16)(17) to the three random graph models we study here allow us to relate the average value of a…”

Section: General Scaling Of Sombor Indices On Random Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Normalized Sombor indices as complexity measures of random graphs

Aguilar-Sanchez,

Mendez-Bermudez,

Rodriguez

et al. 2021

Preprint

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show abstract

“…The following bounds of p-Sombor energy are similar to the (reduced) Sombor energy of Theorem 5.4 of [34], we omit the proof.…”

Section: Bounds Of P-sombor Energy and P-sombor Estrada Indexmentioning

confidence: 86%

Spectral properties of $p$-Sombor matrices and beyond

Liu¹,

You²,

Huang³

et al. 2021

Preprint

Self Cite

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Let G = (V (G), E(G)) be a simple graph with vertex setand 0 otherwise, where d i denotes the degree of vertex v i in G. In this paper, we study the relationship between p-Sombor index SO p (G) and p-Sombor matrix S p (G) by the k-th spectral moment N k and the spectral radius of S p (G). Then we obtain some bounds of p-Sombor Laplacian spectrum, p-Sombor spectral radius, p-Sombor spectral spread, p-Sombor energy and p-Sombor Estrada index. We also investigate the Nordhaus-Gaddum-type results for p-Sombor spectral radius and energy. At last, we give the regression model for boiling point and some other invariants.

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“…The results indicate that the Sombor index may be successfully applied for the modeling of thermodynamic properties of compounds and confirm the suitability of this new index in QSPR analysis. For more chemical applications, the readers may see in [12][13][14] for reference. K. C. Das et al [15,16] obtained some lower and upper bounds on SO in terms of graph parameters.…”

Section: Introductionmentioning

confidence: 99%

More on Sombor Index of Graphs

2022

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Recently, a novel degree-based molecular structure descriptor, called Sombor index was introduced. Let G=(V(G),E(G)) be a graph. Then, the Sombor index of G is defined as SO(G)=∑uv∈E(G)dG2(u)+dG2(v). In this paper, we give some lemmas that can be used to compare the Sombor indices between two graphs. With these lemmas, we determine the graph with maximum SO among all cacti with n vertices and k cut edges. Furthermore, the unique graph with maximum SO among all cacti with n vertices and p pendant vertices is characterized. In addition, we find the extremal graphs with respect to SO among all quasi-unicyclic graphs.

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Ordering chemical graphs by Sombor indices and its applications

Cited by 49 publications

References 10 publications

Normalized Sombor indices as complexity measures of random graphs

Normalized Sombor indices as complexity measures of random graphs

Spectral properties of $p$-Sombor matrices and beyond

More on Sombor Index of Graphs

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