The number of spanning trees in a prism

Boesch, Francis T.; Bogdanowicz, Zbigniew R.

doi:10.1080/00207168708803568

Cited by 27 publications

(19 citation statements)

References 4 publications

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“…Since then, a lot of papers devoted to the complexity of various classes of graphs were published. In particular, explicit formulae were obtained for complete multipartite graphs [5,2], almost complete graphs [25], wheels [3], fans [8], prisms [4], ladders [19], Möbius ladders [20], lattices [26,21,11], anti-prisms [24], complete prisms [18] and for many other families.…”

Section: Introductionmentioning

confidence: 99%

On Rationality of Generating Function for the Number of Spanning Trees in Circulant Graphs

Mednykh

2020

Algebra Colloq.

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Let F (x) = ∞ n=1 τ (n)x n be the generating function for the number τ (n) of spanning trees in the circulant graphs C n (s 1 , s 2 , . . . , s k ). We show that F (x) is a rational function with integer coefficients satisfying the property F (x) = F (1/x). A similar result is also true for the circulant graphs of odd valency C 2n (s 1 , s 2 , . . . , s k , n). We illustrate the obtained results by a series of examples.

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Section: Introductionmentioning

confidence: 99%

On Rationality of Generating Function for the Number of Spanning Trees in Circulant Graphs

Mednykh

2020

Algebra Colloq.

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“…Since then, a lot of papers devoted to the complexity of various classes of graphs were published. In particular, explicit formulae were derived for complete multipartite graphs [7,3], almost complete graphs [35], wheels [4], fans [12], prisms [5], ladders [27], Möbius ladders [28], lattices [29], anti-prisms [33], complete prisms [26] and for many other families. For the circulant graphs some explicit and recursive formulae are given in [37,38,39,40,41,42].…”

Section: Introductionmentioning

confidence: 99%

The number of spanning trees in circulant graphs, its arithmetic properties and asymptotic

Mednykh

2019

Discrete Mathematics

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In this paper, we develop a new method to produce explicit formulas for the number τ (n) of spanning trees in the undirected circulant graphs C n (s 1 , s 2 , . . . , s k ) and C 2n (s 1 , s 2 , . . . , s k , n). Also, we prove that in both cases the number of spanning trees can be represented in the form τ (n) = p n a(n) 2 , where a(n) is an integer sequence and p is a prescribed natural number depending on the parity of n. Finally, we find an asymptotic formula for τ (n) through the Mahler measure of the associated Laurent polynomial L(z) = 2k − k i=1 (z s i + z −s i ).

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“…There are many methods on calculating the number of spanning trees, such as enumerating the subgraphs, 16 dual graphs, 17 Laplacian spectrum, 18 and matrix-tree theorem. 19 In Ref. 20, Dorogovtsev et al firstly proposed the pseudofractal web and investigated the topological properties.…”

Section: Introductionmentioning

confidence: 99%

Enumeration of Spanning Trees on Generalized Pseudofractal Networks

2015

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In this paper, we calculate the number of spanning trees on two families of generalized pseudofractal networks with two controllable parameters. The initial state is a complete graph with an arbitrary number of nodes as a generalization of a triangle. In the subsequent steps, each existing edge (newly produced edge) gives birth to finite new nodes. Using the electrically equivalent transformations, we obtain the changes of edge weights of corresponding equivalent networks and derive the relationships for enumerating spanning trees between original networks and transformed networks. Finally, we obtain closed-form formulas for the number of spanning trees, which is verified by numerical simulations.

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The number of spanning trees in a prism

Cited by 27 publications

References 4 publications

On Rationality of Generating Function for the Number of Spanning Trees in Circulant Graphs

On Rationality of Generating Function for the Number of Spanning Trees in Circulant Graphs

The number of spanning trees in circulant graphs, its arithmetic properties and asymptotic

Enumeration of Spanning Trees on Generalized Pseudofractal Networks

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