Tutte Polynomials of Two Self-similar Network Models

Liao, Yunhua; Xie, Xiao-Liang; Hou, Yaoping; Aziz-Alaoui, M. A.

doi:10.1007/s10955-018-2204-9

Cited by 7 publications

(6 citation statements)

References 28 publications

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“…In section 4, we examine the self-similar network N(t) presented in [1] as another application of the underlying model M(t). We deduce the Tutte polynomial of N(t) by applying some results published in [29]. The number of spanning trees of N(t) is explicitly derived and coincided with the results obtained by using Matlab code which enhances the validity of them.…”

Section: Introductionsupporting

confidence: 62%

“…As presented, the network model N(t), studied in [1], is obtained from the network model M(t) by replacing each edge in M(t) by a path of length two. We can also deduce the Tutte polynomial of N(t) by the aid of the Tutte polynomial of M(t) based on the results published in [29]. We shall rely on the work achieved by Y. Liao et al [29] to compute the Tutte polynomial of model N(t).…”

Section: Number Of Spanning Trees Of Model M(t)mentioning

confidence: 99%

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Tutte polynomial of self-similar network models with applications

Aboutahoun,

El-Safty

2023

Ars Comb.

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Determining the Tutte polynomial T ( G ; x , y ) of a graph network G is a challenging problem for mathematicians, physicians, and statisticians. This paper investigates a self-similar network model M ( t ) and derives its Tutte polynomial. In addition, we evaluate exact explicit formulas for the number of acyclic orientations and spanning trees of it as applications of the Tutte polynomial. Finally, we use the derived T ( M ( t ) ; x , y ) to obtain the Tutte polynomial of another self-similar model N ( t ) presented in [1] and correct the main result discussed in [1] by Ma et al. and test our result numerically by using Matlab.

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Section: Introductionsupporting

confidence: 62%

Section: Number Of Spanning Trees Of Model M(t)mentioning

confidence: 99%

Tutte polynomial of self-similar network models with applications

Aboutahoun,

El-Safty

2023

Ars Comb.

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“…One such graph-theoretical parameter is the multiplicative degree-Kirchhoff index (see [1]). In statistical physics (see [2]), the enumeration of spanning trees in a graph is a crucial problem. It is interesting to note that the multiplicative degree-Kirchhoff index is closely related to the number of spanning trees in a graph.…”

Section: Introductionmentioning

confidence: 99%

Computing the Normalized Laplacian Spectrum and Spanning Tree of the Strong Prism of Octagonal Network

Ahamad

Ali

Siddique

et al. 2022

Journal of Mathematics

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Spectrum analysis and computing have expanded in popularity in recent years as a critical tool for studying and describing the structural properties of molecular graphs. Let O n 2 be the strong prism of an octagonal network O n . In this study, using the normalized Laplacian decomposition theorem, we determine the normalized Laplacian spectrum of O n 2 which consists of the eigenvalues of matrices ℒ A and ℒ S of order 3 n + 1 . As applications of the obtained results, the explicit formulae of the degree-Kirchhoff index and the number of spanning trees for O n 2 are on the basis of the relationship between the roots and coefficients.

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“…The number of spanning trees in graphs is a very important and attractive quantity in both statistical mechanics and physical systems . Spanning trees are closely related to many aspects of the network, including random walks, transportation, optimal Synchronization, and reliability .…”

Section: Introductionmentioning

confidence: 99%

Study on the normalized Laplacian of a penta‐graphene with applications

Zaman

Sun

et al. 2020

Int J of Quantum Chemistry

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Let L n denote a linear pentagonal chain with 2n pentagons. The penta‐graphene (penta‐C), denoted by R n is the graph obtained from L n by identifying the opposite lateral edges in an ordered way, whereas the pentagonal Möbius ring Rn′ is the graph obtained from the L n by identifying the opposite lateral edges in a reversed way. In this paper, through the decomposition theorem of the normalized Laplacian characteristic polynomial and the relationship between its roots and the coefficients, an explicit closed‐form formula of the multiplicative degree‐Kirchhoff index (resp. Kemeny's constant, the number of spanning trees) of R n is obtained. Furthermore, it is interesting to see that the multiplicative degree‐Kirchhoff index of R n is approximately 13 of its Gutman index. Based on our obtained results, all the corresponding results are obtained for Rn′.

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Tutte Polynomials of Two Self-similar Network Models

Cited by 7 publications

References 28 publications

Tutte polynomial of self-similar network models with applications

Tutte polynomial of self-similar network models with applications

Computing the Normalized Laplacian Spectrum and Spanning Tree of the Strong Prism of Octagonal Network

Study on the normalized Laplacian of a penta‐graphene with applications

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