# IJPAM: Volume 32, No. 4 (2006)

A CONJECTURE OF CLAW-FREE HAMILTONIAN GRAPHS
WITH NEIGHBORHOOD UNION

Kewen Zhao
Department of Mathematics
University of Qiongzhou
Wuzhishan, Hainan, 572200, P.R. CHINA
e-mail: kewen@bxemail.com

Abstract.R.J. Faudree et al obtained that if is a 3-connected claw-free graph of order , and for each pair of nonadjacent vertices , , then is Hamiltonian. They conjectured that if is a 3-connected claw-free graph of order , and for each pair of nonadjacent vertices , , then is Hamiltonian. This paper we prove that if is a 3-connected claw-free graph of order , and for each pair of nonadjacent vertices , , then is Hamiltonian.