Enumeration of spanning trees in the sequence of Dürer graphs

• Autorzy: Shixing Li
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Spanning trees; Electrically equivalent transformation; Entropy

Kategorie tematyczne

• 05C30: Enumeration in graph theory
• 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
• 05C63: Infinite graphs

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1591-1598

Daty

wydano

2017-01-01

otrzymano

2016-10-12

zaakceptowano

2017-12-07

online

2017-12-29

Twórcy

autor

Shixing Li

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Identyfikatory

DOI

10.1515/math-2017-0136