Some sufficient conditions on hamilton graphs with toughness - Cai, Gaixiang; Yu, Tao; Xu, Huan; Yu, Guidong (Frontiers in Computational Neuroscience, 2022)
Let G be a graph, ω(G) denote the number of components of a graph G, and t is real number. If ω(G-S)2 |S|tω(G-S) holds for each set S of vertex set (G) of G, G be said to be t-tough. The toughness of G is the maximum value of t for which G is t-tough, denoted with τ(G). The graph G is called Hamilton graph if it has a cycle which contains all vertices of G. Chvatal and other scholars have studied the relation between toughness conditions to the existence of cycle structures. In this paper, we first establish some sufficient conditions for a graph with toughness to be Hamiltonian in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph.