# 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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topShixing 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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