Entropy and enumeration of spanning connected unicyclic subgraphs in self-similar network
Physica A: Statistical Mechanics and its Applications, ISSN: 0378-4371, Vol: 590, Page: 126772
2022
- 1Citations
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Article Description
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.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0378437121009584; http://dx.doi.org/10.1016/j.physa.2021.126772; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85122086012&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0378437121009584; https://dx.doi.org/10.1016/j.physa.2021.126772
Elsevier BV
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