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Wiener-type invariants of pancyclicity for t-tough graphs
Ma,Tingyan van Dam,Edwin R. Wang,Ligong
Ma,Tingyan
van Dam,Edwin R.
Wang,Ligong
Abstract
A connected graph G is t-tough if t <middle dot> c(G-S) <= |S| for every vertex cut S of G, where c(G-S) is the number of components of G-S. A graph G is called pancyclic if it has cycles of all lengths from 3 to n. A Wiener-type invariant of a connected graph G is defined as Wf = Sigma u,vEV(G)f(dG(u, v)), where f(x) is a nonnegative function on the distance dG(u, v). In this paper, we present the best possible Wiener-type conditions to guarantee a ttough graph to be pancyclic in the case when t E {1, 2, 3}. Furthermore, we determine sufficient conditions on the distance and distance signless Laplacian spectral radius for a graph to be pancyclic. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Description
Date
2026-01
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
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Keywords
Distance matrix, Distance signless Laplacian matrix, Pancyclic, Wiener-type invariants
Citation
Ma, T, van Dam, E R & Wang, L 2026, 'Wiener-type invariants of pancyclicity for t-tough graphs', Discrete Applied Mathematics, vol. 379, pp. 575-585. https://doi.org/10.1016/j.dam.2025.10.010