On toughness and fractional (g,f,n )-critical graphs

  • Authors:

  • Shuli Liu

  • Affiliations:

  • School of Mathematics and Information Sciences, Weifang University, Weifang 261061, PR China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2010

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Abstract

Let G be a graph with vertex set V(G). For any S@?V(G) we use @w(G-S) to denote the number of components of G-S. The toughness of G, t(G), is defined as t(G)=min{|S|/@w(G-S)|S@?V(G),@w(G-S)1} if G is not complete; otherwise, set t(G)=+~. In this paper, we consider the relationship between the toughness and fractional (g,f,n)-critical graphs. It is proved that a graph G is a (g,f,n)-critical graph if t(G)=(b^2-1)(n+1)/a.