DIMENSI METRIK LOKAL PADA GRAF MUSICAL DAN GRAF STACKED PRISM

Abstract

Abstract:For example G is a connected and nontrivial graph. The distance between two vertices u and v in G is the shortest path between vertex u and v which is denoted by d (u, v). Suppose that there is a sequential set of  of vertex n which is different from G, then the representation of vertex v to W is a sequential pair of . The set W is called as local distinguishing set if for each pair of vertex u and v is adjacent to G. The local distinguishing set W with minimum cardinality is called as local metric base and its cardinality is called as local metric dimension of graph G denoted by . In this research, metric local dimension of Musical MGn and stacked prism graphs Ym is determined.  This is literature study by combining relevant references. The results state that local metric dimension in musical graphs is  for n and  for n > 3. Local metric dimension in stacked prism graph is  for even m and  for odd m.

Keywords: local metric dimension, musical graph, stacked prism graph, local distinguishing set.