Spectral Radius and Hamiltonicity of graphs

摘要

In this paper, we study the Hamiltonicity of graphs with large minimumdegree. Firstly, we present some conditions for a simple graph to beHamilton-connected and traceable from every vertex in terms of the spectralradius of the graph or its complement respectively. Secondly, we give theconditions for a nearly balanced bipartite graph to be traceable in terms ofspectral radius, signless Laplacian spectral radius of the graph or itsquasi-complement respectively.