Locating-total domination in claw-free cubic graphs

Michael A. Henning, Christian Löwenstein

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)

Abstract

In this paper, we continue the study of locating-total domination in graphs. A set S of vertices of a graph G is a total dominating set of G if every vertex of G is adjacent to a vertex in S. We consider total dominating sets S which have the additional property that distinct vertices in V(G)\S are totally dominated by distinct subsets of the total dominating set. Such a set S is called a locating-total dominating set in G, and the locating-total domination number of G is the minimum cardinality of a locating-total dominating set in G. A claw-free graph is a graph that does not contain K 1,3 as an induced subgraph. We show that the locating-total domination number of a claw-free cubic graph is at most one-half its order and we characterize the graphs achieving this bound.

Original languageEnglish
Pages (from-to)3107-3116
Number of pages10
JournalDiscrete Mathematics
Volume312
Issue number21
DOIs
Publication statusPublished - 6 Nov 2012

Keywords

  • Claw-free
  • Cubic
  • Locating-total domination
  • Total domination

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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