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

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  • Guo, Songlin
  • Wang, Wei
  • Wang, Chuanming

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.

Suggested Citation

  • Guo, Songlin & Wang, Wei & Wang, Chuanming, 2023. "Disproof of a conjecture on the minimum Wiener index of signed trees," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    • Handle: RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006518
    DOI: 10.1016/j.amc.2022.127577
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    1. Spiro, Sam, 2022. "The Wiener index of signed graphs," Applied Mathematics and Computation, Elsevier, vol. 416(C).
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