J4 ›› 2011, Vol. 24 ›› Issue (2): 1-5.

• Content •     Next Articles

A neighborhood condition of a super -λk trianglefree graph

 HUANG Li, GAO Jing-Zhen   

  1. School of Mathematics, Shandong Normal University, Jinan 250014, China
  • Received:2010-09-08 Online:2011-04-20 Published:2011-04-20

Abstract:

Let  k be a positive integer, and G be a connected trianglefree graph of order n≥2k. We prove that  G is a superk graph or Kk+1,n-k-1 if each pair of nonadjacent vertices u,v satisfy |N(u)∩N(v)|≥k+1.This result can be applied to the analysis of network reliability.

Key words: graph, restricted edge connectivity, super -λk graph

CLC Number: 

  • O157.5