Enumeration of spanning trees on contact graphs of disk packings

Qin, Sen; Zhang, Jingyuan; Chen, Xufeng; Chen, Fangyue

doi:10.1016/j.physa.2015.03.047

Cited by 8 publications

(3 citation statements)

References 36 publications

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“…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%

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

2019

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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.

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Section: Introductionmentioning

confidence: 99%

“…In this paper, inspired by the work in [13,24], we investigate the number of spanning trees in a hybrid network proposed by Zhang et al [25], which follows an exponential degree distribution and has a small-world effect. Unlike many other deterministic networks, the hybrid network is not selfsimilar.…”

Section: Introductionmentioning

confidence: 99%

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

2019

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“…Recently, the enumeration of spanning trees has been investigated by the electrically equivalent transformations in Refs. [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Enumeration of spanning trees in the sequence of Dürer graphs

2017

Open Mathematics

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Abstract:In this paper, we calculate the number of spanning trees in the sequence of Dürer graphs with a special feature that it has two alternate states. Using the electrically equivalent transformations, we obtain the weights of corresponding equivalent graphs and further derive relationships for spanning trees between the Dürer graphs and transformed graphs. By algebraic calculations, we obtain a closed-form formula for the number of spanning trees with regard to iteration step. Finally we compare the entropy of our graph with other studied graphs and see that its value of entropy lies in the interval of those of graphs with average degree being 3 and 4.

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On constructing rational spanning tree edge densities

Kahl

2016

Discrete Applied Mathematics

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Enumeration of spanning trees on contact graphs of disk packings

Cited by 8 publications

References 36 publications

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

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

Enumeration of spanning trees in the sequence of Dürer graphs

On constructing rational spanning tree edge densities

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