Enumeration of subtrees of planar two-tree networks

Daoqiang Sun, Long Li, Kai Liu, Hua Wang and Yu Yang

Applied Mathematics and Computation, 2022, vol. 434, issue C

Abstract: The number of subtrees, also referred to as the subtrees index, is a key parameter to measure graph structures such as networks. In this paper, we investigate the number of subtrees of planar two-tree networks. By “adding a virtual edge” and “edge orientation”, we present a linear time algorithm for computing the number of subtrees of planar two-tree networks, as well as a family of planar two-connected networks. As applications, we provide the formulae for the number of subtrees of the famous small-world Farey network and GDURT network. We also discuss the relationship between the spanning subtree number and the subtree number of these networks.

Keywords: Subtree; Planar two-tree networks; Planar two-connected networks; Virtual edge; Edge orientation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322004787

DOI: 10.1016/j.amc.2022.127404

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