Spectral Radius and Hamiltonicity of Graphs

Abstract

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

Keywords

• spectral radius
• singless laplacian spectral radius
• traceable
• hamiltonian-connected
• traceable from every vertex
• minimum degree
• 05c50
• 05c45
• 05c35