Iswadi, Hazrul
(2011)
*Locating and Total Dominating Sets of Direct Products of Complete Graphs.*
Proceeding of 3rd International Conferences and Workshops on Basic and Applied Sciences 2011 (ICOWOBAS 2011).
pp. 585-589.
ISSN 978-979-19096-1-7

Preview |
PDF
hazrul_Locating and Total Dominating Sets_2011.pdf Download (220kB) | Preview |

## Abstract

A set S of vertices in a graph G = (V,E) is a metric-locating-total dominating set of G if every vertex of V is adjacent to a vertex in S and for every u ≠ v in V there is a vertex x in S such that d(u,x) ≠ d(v,x). The metric-location-total domination number \gamma^M_t(G) of G is the minimum cardinality of a metric-locating-total dominating set in G. For graphs G and H, the direct product G × H is the graph with vertex set V(G) × V(H) where two vertices (x,y) and (v,w) are adjacent if and only if xv in E(G) and yw in E(H). In this paper, we determine the lower bound of the metric-location-total domination number of the direct products of complete graphs. We also determine some exact values for some direct products of two complete graphs.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | metric-locating-total dominating set, metric-location-total domination number, direct product |

Subjects: | Q Science > Q Science (General) |

Divisions: | Academic Department > Department of Mathematics and Natural Science |

Depositing User: | Hazrul Iswadi 6179 |

Date Deposited: | 29 Mar 2012 05:39 |

Last Modified: | 24 Mar 2021 14:17 |

URI: | http://repository.ubaya.ac.id/id/eprint/274 |

### Actions (login required)

View Item |