Abstract:

Let G be a simple graph, A(G), Q(G) and Q(G) are the adjacency matrix, the signless Laplacian matrix, and the distance signless Laplacian matrix of G, respectively. The largest eigenvalues of A(G), Q(G) and Q(G) are called the spectral radius, the signless Laplacian spectral radius and the distance signless Laplacian spectral radius of G, respectively. A path is called a Hamilton path if it contains all vertices of G. A graph is traceable if it contains a Hamilton path. A graph is traceable from every vertex if it contains a Hamilton path from every vertex. The main research of this paper is to give some sufficient conditions for a graph to be traceable from every vertex in terms of spectral radius, signless Laplacian spectral radius and distance signless Laplacian spectral radius of the graph, respectively.

Key words: traceable from every vertex, spectral radius, signless Laplacian spectral radius, distance signless Laplacian spectral radius