Dimensi Metrik Graf Kr+mKsr, m, r, s, En

Abstract

The concept of minimum resolving set has proved to be useful and or related to a variety of fields such as Chemistry, Robotic Navigation, and Combinatorial Search and Optimization. So that, this thesis explains the metric dimension of graph Kr + mKsr, m, r, s E N. Resolving set of a graph G is a subset of F (G) that its distance representation is distinct to all vertices of graph G. Resolving set with minimum cardinality is called minimum resolving set, and cardinal states metric dimension of G and noted with dim (G). By drawing the graph, it will be found the resolving set, minimum resolving set and the metric dimension easily. After that, formulate those metric dimensions into a theorem. This research search for the metric dimension of Kr + mKs, m > 2, m,r,s E N and its outcome are dim (Kr + mK1)= m+ (r-2) and dim(Kr + mKs)= m(s-1)+(r-2). This research can be continued for determining the metric dimension of another graph, by changing the operation of its graph or partition graph.