AUTHOR=Cai Gaixiang , Yu Tao , Xu Huan , Yu Guidong 

TITLE=Some sufficient conditions on hamilton graphs with toughness

JOURNAL=Frontiers in Computational Neuroscience

VOLUME=16

YEAR=2022

URL=https://www.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2022.1019039

DOI=10.3389/fncom.2022.1019039

ISSN=1662-5188

ABSTRACT=<p>Let <italic>G</italic> be a graph, and the number of components of <italic>G</italic> is denoted by <italic>c</italic>(<italic>G</italic>). Let <italic>t</italic> be a positive real number. A connected graph <italic>G</italic> is <italic>t</italic>-tough if <italic>tc</italic>(<italic>G</italic> − <italic>S</italic>) ≤ |<italic>S</italic>| for every vertex cut <italic>S</italic> of <italic>V</italic>(<italic>G</italic>). The <italic>toughness</italic> of <italic>G</italic> is the largest value of <italic>t</italic> for which <italic>G</italic> is <italic>t</italic>-tough, denoted by τ(<italic>G</italic>). We call a graph <italic>G</italic> Hamiltonian if it has a cycle that contains all vertices of <italic>G</italic>. Chvátal and other scholars investigate the relationship between toughness conditions and the existence of cyclic structures. In this paper, we establish some sufficient conditions that a graph with toughness is Hamiltonian based on the number of edges, spectral radius, and signless Laplacian spectral radius of the graph.</p><p><bold>MR subject classifications:</bold> 05C50, 15A18.</p>