A neighborhood condition for graphs to be maximally k-restricted edge connected

  • Authors:

  • Shiying Wang;Lei Zhang;Shangwei Lin

  • Affiliations:

  • School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China;School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China;School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, PR China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2012

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Abstract

For a connected graph G=(V,E), an edge set S@?E is a k-restricted edge cut if G-S is disconnected and every component of G-S has at least k vertices. The k-restricted edge connectivity of G, denoted by @l"k(G), is defined as the cardinality of a minimum k-restricted edge cut. Let @x"k(G)=min{|[X,X@?]|:|X|=k,G[X]is connected}. G is @l"k-optimal if @l"k(G)=@x"k(G). Let k=4 be an integer. In this paper, we show that if |N"G(u)@?N"G(v)|=k for all pairs u,v of non-adjacent vertices and @x"k(G)=