Characterization of minimally (2,l)-connected graphs

  • Authors:

  • Xiaofeng Gu;Hong-Jian Lai;Senmei Yao

  • Affiliations:

  • Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, PR China and Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA;Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA

  • Venue:
  • Information Processing Letters
  • Year:
  • 2011

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Abstract

For an integer l=2, the l-connectivity @k"l(G) of a graph G is defined to be the minimum number of vertices of G whose removal produces a disconnected graph with at least l components or a graph with fewer than l vertices. Let k=1, a graph G is called (k,l)-connected if @k"l(G)=k. A graph G is called minimally (k,l)-connected if @k"l(G)=k but @?e@?E(G), @k"l(G-e)=