The number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs

被引：26
|
作者：
Comellas, Francesc [1 ]
Miralles, Alicia [1 ]
Liu, Hongxiao [2 ]
Zhang, Zhongzhi [2 ]
机构：
[1] Univ Politecn Cataluna, EPSC, Dep Matemat Aplicada 4, E-08028 Barcelona, Catalonia, Spain
[2] Fudan Univ, Sch Comp Sci, Shanghai Key Lab Intelligent Informat Proc, Shanghai 200433, Peoples R China
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2013年 / 392卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Spanning trees; Tree entropy; Complex networks; Self-similarity; ENUMERATION;
D O I：
10.1016/j.physa.2012.10.047
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper we give an exact analytical expression for the number of spanning trees of an infinite family of outerplanar, small-world and self-similar graphs. This number is an important graph invariant related to different topological and dynamic properties of the graph, such as its reliability, synchronization capability and diffusion properties. The calculation of the number of spanning trees is a demanding and difficult task, in particular for large graphs, and thus there is much interest in obtaining closed expressions for relevant infinite graph families. We have also calculated the spanning tree entropy of the graphs which we have compared with those for graphs with the same average degree. (c) 2013 Elsevier B.V. All rights reserved.
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页码：2803 / 2806
页数：4
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