Neighborhood conditions for graphs to be super restricted edge connected

  • Authors:

  • Shiying Wang;Jing Li;Lihong Wu;Shangwei Lin

  • Affiliations:

  • School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China;School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China;School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China;School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China

  • Venue:
  • Networks
  • Year:
  • 2010

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Abstract

Restricted edge connectivity is a more refined network reliability index than edge connectivity. For a connected graph G = (V, E), an edge set S ⊆ E is a restricted edge cut if G - S is disconnected and every component of G - S has at least two vertices. The restricted edge connectivity of G is defined as the cardinality of a minimum restricted edge cut. G is super restricted edge connected if every minimum restricted edge cut of G isolates one edge. In this article, we present several neighborhood conditions for a graph to be super restricted edge connected. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010