On the spectral radius, energy and Estrada index of the arithmetic–geometric matrix of a graph

Lin, Zhen; Deng, Bo; Miao, Lianying; Li, He

doi:10.1142/s1793830921501081

Cited by 8 publications

(6 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Results of Theorem 4.1, Theorem 4.6 and Theorem 4.7 extend the results of [30]. In the following, we consider the bounds of p-Sombor spectral spread of G.…”

Section: Introductionsupporting

confidence: 56%

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.

show abstract

“…Results of Theorem 4.1, Theorem 4.6 and Theorem 4.7 extend the results of [30]. In the following, we consider the bounds of p-Sombor spectral spread of G.…”

Section: Introductionsupporting

confidence: 56%

Spectral properties of p-Sombor matrices and beyond

Liu¹,

You²,

Huang³

et al. 2021

match

View full text Add to dashboard Cite

show abstract

“…Since

we have

where the equation

holds if and only if

which is possible if and only if

and

Thus, G has three distinct modified Sombor eigenvalues and hence, according to Proposition 1.3.3 of [ 40 ], the diameter of G must be two. Moreover, we note that the modified Sombor spectrum of G is symmetric toward the origin, so it is verified that G is bipartite (see Lemma 2.12 of [ 22 ]). Consequently, it follows that G is a complete bipartite graph (see Theorem 2.1 of [ 41 ] and Corollary 3.8 of [ 43 ]).…”

Section: Results Concerning the Modified Sombor Matrixmentioning

confidence: 76%

“…The graph energy

has its origin in theoretical chemistry and helps in approximating the

-electron energy of unsaturated hydrocarbons. There is a wealth of literature about graph energy and its related topics (for examples, see [ 19 , 20 , 21 , 22 , 23 , 24 , 25 ]).…”

Section: Introductionmentioning

confidence: 99%

“…Two graphs with the same modified Sombor energy are referred to as modified Sombor equienergetic graphs . Various papers on the spectral properties of the Sombor matrix, involving Sombor eigenvalues, the Sombor spectral radius, Sombor energy, the Sombor Estrada index, the relation of energy with Sombor energy, and the Sombor index, have recently been published (for examples, see [ 22 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ]).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Some Topological Indices Defined via the Modified Sombor Matrix

et al. 2022

View full text Add to dashboard Cite

Let G be a simple graph with the vertex set V={v1,…,vn} and denote by dvi the degree of the vertex vi. The modified Sombor index of G is the addition of the numbers (dvi2+dvj2)−1/2 over all of the edges vivj of G. The modified Sombor matrix AMS(G) of G is the n by n matrix such that its (i,j)-entry is equal to (dvi2+dvj2)−1/2 when vi and vj are adjacent and 0 otherwise. The modified Sombor spectral radius of G is the largest number among all of the eigenvalues of AMS(G). The sum of the absolute eigenvalues of AMS(G) is known as the modified Sombor energy of G. Two graphs with the same modified Sombor energy are referred to as modified Sombor equienergetic graphs. In this article, several bounds for the modified Sombor index, the modified Sombor spectral radius, and the modified Sombor energy are found, and the corresponding extremal graphs are characterized. By using computer programs (Mathematica and AutographiX), it is found that there exists only one pair of the modified Sombor equienergetic chemical graphs of an order of at most seven. It is proven that the modified Sombor energy of every regular, complete multipartite graph is 2; this result gives a large class of the modified Sombor equienergetic graphs. The (linear, logarithmic, and quadratic) regression analyses of the modified Sombor index and the modified Sombor energy together with their classical versions are also performed for the boiling points of the chemical graphs of an order of at most seven.

show abstract

“…By Perron-Frobenius theorem,

is unique with

and the corresponding eigenvector Y of

have positive entries. The trace norm (Sombor energy of G ) is

Several interesting papers on spectral properties of

, like the results on Sombor spectrum, the Sombor energy

, the Sombor Estrada index, connections of trace norm of

with

and others spectral invariants can be seen in [4] , [18] , [19] , [21] , [23] , [24] , [31] . The spread (Sombor spectral spread) of

is defined as

.…”