The minimum Wiener index of unicyclic graphs with maximum degree

Shan Zhang, Xun Chen, Zhen-Wei Ma, Xiao-Dong Zhang and Ya-Hong Chen

Applied Mathematics and Computation, 2024, vol. 470, issue C

Abstract: For a graph G, the Wiener index W(G) is the sum of distances between all pairs of vertices, which is one of the most popular graph invariants. In this paper, we characterize a class of the unicyclic graphs with given order n and maximum degree Δ which minimize Wiener index, and then identify a class of the unicyclic graphs with g=3 and Δ⩾4 which minimize Wiener index.

Keywords: Wiener index; Unicyclic graph; T-unicyclic-graph; Hanging tree (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000535

DOI: 10.1016/j.amc.2024.128581

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