## 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 language | English |
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Pages (from-to) | 3107-3116 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 312 |

Issue number | 21 |

DOIs | |

Publication status | Published - 6 Nov 2012 |

## Keywords

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

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics