Sombor index: review of extremal results and bounds

Liu, Hechao; Gutman, Ivan; You, Lihua; Huang, Yufei

doi:10.1007/s10910-022-01333-y

Cited by 53 publications

(18 citation statements)

References 39 publications

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“…Redžepović [6] examined the predictive and discriminative potentials of the Sombor and reduced Sombor indices of chemical graphs and showed that these molecular descriptors have good predictive potential. In a recent paper [7], Liu et al reviewed the existing bounds and extremal results related to the Sombor index and its variants.…”

Section: Introductionmentioning

confidence: 99%

Comparisons of the Sombor Index of Alkane, Alkyl, and Annulene Series with Their Molecular Mass

Mohammadi

Barzegar

Ashrafi

2022

Journal of Chemistry

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Suppose G is an undirected simple graph. A topological index for G is a number with this property that it is invariant under all graph isomorphisms with applications in chemistry. The Sombor and reduced Sombor indices of G are defined as S O G = ∑ u v ∈ E G d G 2 u + d G 2 v and S O red G = ∑ u v ∈ E G d G u − 1 2 + d G v − 1 2 , respectively. Here, d G u denotes the degree of the vertex u in G . In this paper, these invariants were computed for alkanes, alkyls, and annulenes. A comparison of our calculations with molecular mass is also presented. As a consequence, it is shown that there is a good correlation between Sombor index and molecular mass of these compounds.

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Section: Introductionmentioning

confidence: 99%

Comparisons of the Sombor Index of Alkane, Alkyl, and Annulene Series with Their Molecular Mass

Mohammadi

Barzegar

Ashrafi

2022

Journal of Chemistry

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“…Te SO index, although proposed recently [5], has received a lot of attention from academics and led to numerous articles; for instance, see the surveys [6,7] and associated references are given therein. Possible chemical applications of the SO index may be found in the papers [8,9].…”

Section: Introductionmentioning

confidence: 99%

On the Maximum Sombor Index of Unicyclic Graphs with a Fixed Girth

Senthilkumar

Venkatakrishnan

Balachandran

et al. 2022

Journal of Mathematics

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Let G be a graph having the set of edges E G . Represent by d G u the degree of a vertex u of G . The Sombor (SO) index of G is defined as SO G = ∑ u v ∈ E G d G u 2 + d G v 2 . The length of a shortest cycle in a graph G is known as the girth of G . A connected graph with the same order and size is usually referred to as a (connected) unicyclic graph. This paper reports the characterization of the graphs possessing the first-two maximum values of the SO index in the class of all (connected) unicyclic graphs with a fixed girth and order.

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“…In [14], Gutman introduced a graph-based topological index named Sombor index. First, it was used in chemistry [15][16][17][18][19][20] and soon after grabbed the attention of mathematicians [21][22][23][24][25][26][27]. Network science used the modeling dynamical e ect of biology and social technological complex systems [28].…”

Section: Introductionmentioning

confidence: 99%

Nirmala and Banhatti‐Sombor Index over Tensor and Cartesian Product of Special Class of Semigroup Graphs

Ünal

2022

Journal of Mathematics

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The Nirmala and first Banhatti-Sombor index which is originated from Sombor index is designated by N G = ∑ u v ∈ E G d u + d v and BSO 1 G = ∑ u v ∈ E G 1 / d u 2 + d v 2 , respectively. In this work, we calculated the Nirmala and Banhatti-Sombor index over the tensor and Cartesian product of a graph of an algebraic structure by presenting two different algorithms.

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Sombor index: review of extremal results and bounds

Cited by 53 publications

References 39 publications

Comparisons of the Sombor Index of Alkane, Alkyl, and Annulene Series with Their Molecular Mass

Comparisons of the Sombor Index of Alkane, Alkyl, and Annulene Series with Their Molecular Mass

On the Maximum Sombor Index of Unicyclic Graphs with a Fixed Girth

Nirmala and Banhatti‐Sombor Index over Tensor and Cartesian Product of Special Class of Semigroup Graphs

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