Shandong Science ›› 2011, Vol. 24 ›› Issue (6): 8-11.doi: 10.3976/j.issn.1002-4026.2011.06.003

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Hamilton cycle of 2-connected P3-dominated graphs

 CHEN Wei-Na, WANG Jiang-Lu   

  1. School of Mathematics, Shandong Normal University, Jinan 250014, China
  • Received:2011-05-17 Published:2011-12-20 Online:2011-12-20

Abstract:

A graph G is a P3-dominated graph if J(x,y)∪J′(x,y)≠Φ for any pair of vertices x and y of d(x,y)=2.This paper proves that for any pair of nonadjacent vertices x and y in G,which is a 2-connected P3-dominated graph of order n no less than 3, if 2|N(x)∪N(y)|+d(x)+d(y)≥2n-5, then G has a Hamilton cycle or G∈{K2,3,K1,1,3}.

Key words: quasi-claw-free graphs, P3-dominated graphs, Hamilton cycle

CLC Number: 

  • O157.5

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