DIMENSI METRIK KETETANGGAAN LOKAL GRAF HASIL OPERASI k-COMB

Abstract

Research on the local adjacency metric dimension has not been found in all operations of the graph, one of them is comb product graph. The purpose of this research was to determine the local adjacency metric dimension of k-comb product graph and level  comb product graph between any connected graph G and H. In this research graph G and graph H such as cycle graph, complete graph, path graph, and star graph. K-comb product graph between any graph G and H denoted by GokH. While level k comb product graph between any graph G and H denoted by GokH.In this research, local adjacency metric dimension of GokSm graph only dependent to multiplication of the cardinality of V(G) and many of k value, while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the cardinality of V(G), many of k value, and local adjacency metric dimension of Km graph or Cm graph. And then, local adjacency metric dimension of GokSm graph only dependent to the cardinality of V(Gok-1Sm), while GokKm graph and GokCm graph is dependent to dominating number of G and multiplication of the local adjacency metric dimension of Km graph or Cm graph with cardinality of V(Gok-1Km) or V(Gok-1Cm).