Enumeration of spanning trees in the sequence of Dürer graphs

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...

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Bibliographic Details
Published inOpen mathematics (Warsaw, Poland) Vol. 15; no. 1; pp. 1591 - 1598
Main Author Li, Shixing
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter Open 29.12.2017
De Gruyter Poland
De Gruyter
Subjects
05C30
05C50
05C63
Electrically equivalent transformation
Entropy
Enumeration
Equivalence
Graph theory
Graphs
Iterative methods
Mathematical analysis
Spanning trees
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Summary: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.
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2017-0136