LOCATING-DOMINATING SET OF HONEYCOMB NETWORK GRAPH - Hardianto, Candra
Architecture of microprocessor networks can be modelled with graphs. The Security of a microprocessor network architecture can be analyzed by using locating-dominating sets. A locating-dominating set is a set ÿ ? ý(ÿ) where for every vertices ÿ, ? ? ý(ÿ) ? ÿ, the neighborhood of vertex ÿ that are members of set S is different from the neighborhood of vertex ? that are members of set S. The minimal cardinality of the set S for a graph ÿ is called the location-domination number of graph G, denoted by ??(ÿ). A honeycomb network graph or ?ÿ(??) is a graph that is formed from the recursion of hexagonal tesselation patterns. In this research, the location-domination number of a ?ÿ(??) graph is determined. In particular, it is proved that ??(?ÿ(??)) is 3,9, and 18 where ?? is 1,2, and 3 respectively. It is also shown that the location-domination number of a ?ÿ(??) graph with ??g 4 does not exceed ??(?ÿ(??2 3)) + 6 + 6(??2 1) + 6(??2 2).