Vertices contained in all or in no minimum total dominating set of a tree

  • Authors:

  • Ernest J. Cockayne;Michael A. Henning;Christina M. Mynhardt

  • Affiliations:

  • Department of Mathematics, University of Victoria, P.O. Box 3045, Victoria, BC, Canada V8W 3P4;School of Mathematics, Statistics and Information Technology, University of Natal, Private Bay X01, Pietermaritzburg 3209, South Africa;Department of Mathematics, University of South Africa, P.O. Box 392, Unisa 0003, South Africa

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2003

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Abstract

A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. We characterize the set of vertices of a tree that are contained in all, or in no, minimum total dominating sets of the tree.