G.-X. Cai, Y.Z Fan, Y. Fang, G.-D. Yu
Spectral radius and Hamiltonicity of graphs
Discussiones Mathematicae Graph Theory
Received 22.09.2017, Revised 10.01.2018, Accepted 10.01.2018, doi: 10.7151/dmgt.2119
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.
spectral radius, singless Laplacian spectral radius, traceable, Hamiltonian-connected, traceable from every vertex, minimum degree