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

Francesc Comellas, Alícia Miralles, Hongxiao Liu and Zhongzhi Zhang

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 12, 2803-2806

Abstract: 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.

Keywords: Spanning trees; Tree entropy; Complex networks; Self-similarity (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:12:p:2803-2806

DOI: 10.1016/j.physa.2012.10.047

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