Entropy and enumeration of spanning connected unicyclic subgraphs in self-similar network

Jing Liang, Haixing Zhao, Jun Yin and Sun Xie

Physica A: Statistical Mechanics and its Applications, 2022, vol. 590, issue C

Abstract: The number of spanning connected unicyclic subgraphs is a critical quantity to characterize the reliability of networks. In 1993, Colbourn in [Colbourn (1993)] proposed a problem about reliability polynomial: Can the number of spanning connected unicyclic subgraphs of a graph be computed efficiently? Up to now, there is no research about this problem. In this paper, we mainly study the entropy and the enumeration of spanning connected unicyclic subgraphs in self-similar networks. We propose a linear algorithm for computing the number of spanning connected unicyclic subgraphs in self-similar network (x, y)-flower. By the algorithm, the exact number of spanning connected unicyclic subgraphs is determined in (x, y)-flower networks. In addition, we define the entropy of spanning connected unicyclic subgraphs and obtain the entropies of spanning connected unicyclic subgraphs in (x, y)-flower networks.

Keywords: The number of spanning connected unicyclic subgraphs; Entropy; (x, y)-flower network (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:590:y:2022:i:c:s0378437121009584

DOI: 10.1016/j.physa.2021.126772

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