Enumeration of Spanning Trees on Generalized Pseudofractal Networks

Xiao, Jinmei; Zhang, Jingyuan; Sun, Weigang

doi:10.1142/s0218348x15500218

Cited by 5 publications

(4 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using these expressions, we have computed the Kirchhoff index, also called the "network criticality", for the categorical product network. The enumeration of spanning trees on generalized pseudofractal networks is discussed in [18]. "…”

Section: Discussionmentioning

confidence: 99%

Laplacian Spectra for Categorical Product Networks and Its Applications

et al. 2018

View full text Add to dashboard Cite

The Kirchhoff index, global mean-first passage time, average path length and number of spanning trees are of great importance in the field of networking. The "Kirchhoff index" is known as a structure descriptor index. The "global mean-first passage time" is known as a measure for nodes that are quickly reachable from the whole network. The "average path length" is a measure of the efficiency of information or mass transport on a network, and the "number of spanning trees" is used to minimize the cost of power networks, wiring connections, etc. In this paper, we have selected a complex network based on a categorical product and have used the spectrum approach to find the Kirchhoff index, global mean-first passage time, average path length and number of spanning trees. We find the expressions for the product and sum of reciprocals of all nonzero eigenvalues of a categorical product network with the help of the eigenvalues of the path and cycles.

show abstract

Section: Discussionmentioning

confidence: 99%

Laplacian Spectra for Categorical Product Networks and Its Applications

et al. 2018

View full text Add to dashboard Cite

show abstract

“…[10] for an application on pseudofractal networks. It is worth noting that we do not assume any symmetry in G.…”

Section: Number Of Spanning Trees Related To Degree Sequencementioning

confidence: 99%

“…Denote by .G/ the number of spanning trees in G. Enumeration of spanning trees in graphs with certain symmetry and fractals has been widely studied via ad hoc techniques capitalizing on the particular structures [6][7][8][9][10][11]. In general, we often have to resort to Kirchhoff's celebrated matrixtree theorem [12], which asserts that n .G/ equals the product of all nonzero eigenvalues of Laplacian matrix of G, i.e., .G/ D 1 n Q n 1 i D1 i .G/.…”

Section: Introductionmentioning

confidence: 99%

On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs

Shang

2016

Open Mathematics

View full text Add to dashboard Cite

As a generalization of the Sierpiński-like graphs, the subdivided-line graph .G/ of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G. In this paper we obtain a closed-form formula for the enumeration of spanning trees in .G/, employing the theory of electrical networks. We present bounds for the largest and second smallest Laplacian eigenvalues of .G/ in terms of the maximum degree, the number of edges, and the first Zagreb index of G. In addition, we establish upper and lower bounds for the Laplacian Estrada index of .G/ based on the vertex degrees of G. These bounds are also connected with the number of spanning trees in .G/.

show abstract

“…In view of their relevance to diverse aspects of networks and a wide range of applications, spanning trees in networks have become a focus of some recent research [12][13][14][15]. Particularly, in the physics literature a lot of effort has been devoted to enumerating spanning trees in specific self-similar networks by using different techniques.…”

Section: Introductionmentioning

confidence: 99%

The number of spanning trees of a hybrid network created by inner-outer iteration

2019

View full text Add to dashboard Cite

We consider the number of spanning trees in a novel hybrid network created by inner-outer iteration. The hybrid network is small-world but not self-similar. Firstly, we introduce two particular electrically equivalent transformations: delta-edge transformation and Sierpinski-delta transformation. By using these two particular transformations, we find the changes of the conductances of corresponding electrically equivalent networks. Secondly, based on the inner-outer iteration structure characteristics, we obtain a closed-form formula for the number of spanning trees of the hybrid network, as well as its spanning tree entropy. Finally, we compare our result with those of previously investigated networks with the same average degree, and give an explanation for their differences.

show abstract

Enumeration of Spanning Trees on Generalized Pseudofractal Networks

Cited by 5 publications

References 23 publications

Laplacian Spectra for Categorical Product Networks and Its Applications

Laplacian Spectra for Categorical Product Networks and Its Applications

On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs

The number of spanning trees of a hybrid network created by inner-outer iteration

Contact Info

Product

Resources

About