| Issue |
EPL
Volume 138, Number 2, April 2022
|
|
|---|---|---|
| Article Number | 22001 | |
| Number of page(s) | 6 | |
| Section | Mathematical and interdisciplinary physics | |
| DOI | https://doi.org/10.1209/0295-5075/ac6904 | |
| Published online | 24 May 2022 | |
Enumerating spanning trees of vertex-edge-growth graph
1 School of Electronics Engineering and Computer Science, Peking University - Beijing 100871, China
2 College of Mathematics and Statistics, Northwest Normal University - Lanzhou 730070, China
(a) mafei123987@163.com (corresponding author)
(b) yybb918@163.com
Received: 3 August 2021
Accepted: 21 April 2022
The problem of determining the number of spanning trees of graph having interesting structural properties such as the scale-free feature is attractive in science community. In this paper, we first present a class of outer-planar and self-similar graphs N(t) by using vertex-edge-growth operation. According to specific topological structure, we calculate the average degree, and show that the model N(t) is sparse. Then, we develop a series of iterative methods in order to obtain an exact solution of the total number of spanning trees of the model N(t), and also illustrate the corresponding spanning tree entropy. The calculation method used can be suitable for enumerating spanning trees of other graphs with similar properties.
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