On the eccentricity matrix of graphs and its applications to the boiling point of hydrocarbons

Wang, Jianfeng; Lei, Xingyu; Wei, Wei; Luo, Xiaobing; Li, Shuchao

doi:10.1016/j.chemolab.2020.104173

Cited by 31 publications

(8 citation statements)

References 11 publications

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“…Entropy, SNar, HNar) of octane isomers and Sombor spectral radius, Sombor energy are shown in Figure 5 From [44], we know that the correction coefficient (R) between boiling ponits of benzenoid hydrocarbons and eccentricity spectral radius is 0.7167, we compare the correction coefficient of Sombor spectral radius, Sombor energy with other spectral radius, energy, we find the Sombor energy (resp. Sombor spectral radius) is also a better predictor.…”

Section: Regression Model For Boiling Point and Some Other Invariantsmentioning

confidence: 99%

Spectral properties of $p$-Sombor matrices and beyond

Liu¹,

You²,

Huang³

et al. 2021

Preprint

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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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Section: Regression Model For Boiling Point and Some Other Invariantsmentioning

confidence: 99%

Spectral properties of $p$-Sombor matrices and beyond

Liu¹,

You²,

Huang³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Entropy, SNar, HNar) of octane isomers of Table 2 are taken from [35] and [15]. With the data of Table 1, scatter plots between BP and Sombor spectral radius, From [43], we know that the correction coefficient (R) between boiling ponits of benzenoid hydrocarbons and eccentricity spectral radius is 0.7167, we compare the correction coefficient of Sombor spectral radius, Sombor energy with other spectral radius, energy, we find the Sombor energy (resp. Sombor spectral radius) is also a better predictor.…”

Section: Regression Model For Boiling Point and Some Other Invariantsmentioning

confidence: 99%

Spectral properties of p-Sombor matrices and beyond

Liu¹,

You²,

Huang³

et al. 2021

match

View full text Add to dashboard Cite

Let G = (V (G), E(G)) be a simple graph with vertex set V (G) = {v 1 , v 2 , • • • , v n } and edge set E(G). The p-Sombor matrix S p (G) of G is the square matrix of order n whose (i, j)-entry is equal to ((d i ) p + (d j ) p ) 1 p if v i ∼ v j , and 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 eigenvalues, 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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“…Wei and Li [17] established a relationship between the majorization and E-spectral radii of complete multipartite graphs. For more details about the eccentricity matrices of graphs,we refer to [2,4,5,10,11,12,13,14,18].…”

Section: Introductionmentioning

confidence: 99%

On the eccentricity matrices of trees: Inertia and spectral symmetry

Mahato¹,

Kannan²

2022

Preprint

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The eccentricity matrix E(G) of a connected graph G is obtained from the distance matrix of G by keeping the largest non-zero entries in each row and each column, and leaving zeros in the remaining ones. The eigenvalues of E(G) are the E-eigenvalues of G. In this article, we find the inertia of the eccentricity matrices of trees. Interestingly, any tree on more than 4 vertices with odd diameter has two positive and two negative E-eigenvalues (irrespective of the structure of the tree). A tree with even diameter has the same number of positive and negative E-eigenvalues, which is equal to the number of 'diametrically distinguished' vertices (see Definition 3.1). Besides we prove that the spectrum of the eccentricity matrix of a tree is symmetric with respect to the origin if and only if the tree has odd diameter. As an application, we characterize the trees with three distinct E-eigenvalues.

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On the eccentricity matrix of graphs and its applications to the boiling point of hydrocarbons

Cited by 31 publications

References 11 publications

Spectral properties of $p$-Sombor matrices and beyond

Spectral properties of $p$-Sombor matrices and beyond

Spectral properties of p-Sombor matrices and beyond

On the eccentricity matrices of trees: Inertia and spectral symmetry

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