2024/06/24 by Vladimir I. Benediktovich, Benediktovich, Vladimir I. · 2 citations
Mathematics · Computer Science · #Graph theory and applications #Advanced Graph Theory Research #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2406.17089
More than 40 years ago Chvátal introduced a new graph invariant, which he called graph toughness. From then on a lot of research has been conducted, mainly related to the relationship between toughness conditions and the existence of cyclic structures, in particular, determining whether the graph is Hamiltonian and pancyclic. A pancyclic graph is certainly Hamiltonian, but not conversely. Bondy in 1976, however, suggested the "metaconjecture" that almost any nontrivial condition on a graph which implies that the graph is Hamiltonian also implies that the graph is pancyclic. We confirm the Bondy conjecture for t-tough graphs in the case when t∈ \ 1;2;3\ in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph.