The number of spanning trees of the Cartesian product of regular graphs
type: Item
instance of: scholarly article
title: The number of spanning trees of the Cartesian product of regular graphs
zbMATH Open document ID: 1407.05057
DOI: 10.1155/2014/750618
author: Mei-Hui Wu
author: Long-Yeu Chung
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The number of spanning trees in graphs or in networks is an important issue. The evaluation of this number not only is interesting from a mathematical (computational) perspective but also is an important measure of reliability of a network or designing electrical circuits. In this paper, a simple formula for the number of spanning trees of the Cartesian product of two regular graphs is investigated. Using this formula, the number of spanning trees of the four well-known regular networks can be simply taken into evaluation.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 7017189
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/750618
OpenAlex ID: W2137003249
Wikidata QID: Q59071931
cites work: On connectivity of the cartesian product of two graphs
cites work: The distinguishing chromatic number of Cartesian products of two complete graphs
cites work: Equitable colorings of Cartesian products of graphs
cites work: Super edge- and point-connectivities of the Cartesian product of regular graphs
cites work: Connectivity of Cartesian product graphs
cites work: Complexity of products of some complete and complete bipartite graphs
cites work: Q4327350
cites work: Q5572939
cites work: Spanning tree formulas and Chebyshev polynomials
cites work: Q4405923
cites work: The number of spanning trees of the generalized Boolean \(n\)-cube network
cites work: On the number of spanning trees in directed circulant graphs
cites work: On the number of spanning trees of multi-star related graphs
cites work: A formula for the number of spanning trees of a multi-star related graph
cites work: The number of spanning trees of the regular networks
cites work: Graph theoretic reliability analysis for the Boolean n cube networks
cites work: The numbers of spanning trees of the cubic cycle \(C_ n^ 3\) and the quadruple cycle \(C_ n^ 4\)
cites work: The number of spanning trees in circulant graphs
cites work: Counting the number of spanning trees in a class of double fixed-step loop networks
cites work: Further analysis of the number of spanning trees in circulant graphs
cites work: The number of spanning trees in directed circulant graphs with non-fixed jumps
cites work: The number of spanning trees in odd valent circulant graphs
cites work: Chebyshev polynomials and spanning tree formulas for circulant and related graphs
cites work: Maximizing the number of spanning trees in \(K_n\)-complements of asteroidal graphs
cites work: The number of spanning trees in \(K_ n\)-complements of quasi-threshold graphs
cites work: The number of spanning trees in a class of double fixed-step loop networks
cites work: A certain polynomial of a graph and graphs with an extremal number of trees
cites work: Q5510744
cites work: Q5622371
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description: scientific article; zbMATH DE number 7017189