Disproof of a conjecture on the minimum Wiener index of signed trees

Songlin Guo, Wei Wang and Chuanming Wang

Applied Mathematics and Computation, 2023, vol. 439, issue C

Abstract: The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices. Sam Spiro [The Wiener index of signed graphs, Appl. Math. Comput., 416(2022)126755] recently introduced the Wiener index for a signed graph and conjectured that the path Pn with alternating signs has the minimum Wiener index among all signed trees with n vertices. By constructing an infinite family of counterexamples, we prove that the conjecture is false whenever n is at least 30.

Keywords: Wiener index; Signed tree; Signed graph (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006518

DOI: 10.1016/j.amc.2022.127577

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