Distance signless Laplacian spectral radius and Hamiltonian properties of graphs

Abstract

In this paper, we establish a sufficient condition on distance signless Laplacian spectral radius for a bipartite graph to be Hamiltonian. 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. Furthermore, we obtain a sufficient condition for a graph to be Hamiltonian in terms of the distance signless Laplacian spectral radius of the complement of a graph G.

Keywords:

• Hamilton-connected
• traceable from every vertex
• distance signless Laplacian spectral radius

AMS Subject Classifications:

• 05C50
• 15A18
• 05C38

Acknowledgements

The authors are grateful to the anonymous referee for his or her valuable comments, suggestions and corrections which improved the presentation of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11171273]; the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University [grant number Z2016170].