# Enumeration of spanning trees in the sequence of Dürer graphs

Open Mathematics (2017)

• Volume: 15, Issue: 1, page 1591-1598
• ISSN: 2391-5455

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## Abstract

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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.

## How to cite

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Shixing Li. "Enumeration of spanning trees in the sequence of Dürer graphs." Open Mathematics 15.1 (2017): 1591-1598. <http://eudml.org/doc/288539>.

@article{ShixingLi2017,
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.},
author = {Shixing Li},
journal = {Open Mathematics},
keywords = {Spanning trees; Electrically equivalent transformation; Entropy},
language = {eng},
number = {1},
pages = {1591-1598},
title = {Enumeration of spanning trees in the sequence of Dürer graphs},
url = {http://eudml.org/doc/288539},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Shixing Li
TI - Enumeration of spanning trees in the sequence of Dürer graphs
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1591
EP - 1598
AB - 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.
LA - eng
KW - Spanning trees; Electrically equivalent transformation; Entropy
UR - http://eudml.org/doc/288539
ER -

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