Distance signless Laplacian spectral radius and Hamiltonian properties of graphs

Abstract

In this paper, first, we establish a sufficient condition for a bipartite graph to be Hamilton-connected. Furthermore, we also give two sufficient conditions on distance signless Laplacian spectral radius for a graph to be Hamilton-connected and traceable from every vertex, respectively. Last, we obtain a sufficient condition for a graph to be Hamiltonian in terms of the distance signless Laplacian spectral radius of $G^{C}$.