The connectivity of a graph and its complement

  • Authors:

  • Angelika Hellwig;Lutz Volkmann

  • Affiliations:

  • Institut für Medizinische Statistik, Universitätsklinikum der RWTH Aachen, Pauwelsstraíe 30, 52075 Aachen, Germany;Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2008

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Abstract

Let G be a graph with minimum degree @d(G), edge-connectivity @l(G), vertex-connectivity @k(G), and let G@? be the complement of G. In this article we prove that either @l(G)=@d(G) or @l(G@?)=@d(G@?). In addition, we present the Nordhaus-Gaddum type result @k(G)+@k(G@?)=min{@d(G),@d(G@?)}+1. A family of examples will show that this inequality is best possible.