DIMENSION PARTITION FULL OF GRAF SUBDIVISION AND FULL OF GRAF BIPARTITE - MULIA HASIBUAN (NIM. 20110027), ISMAIL
The concept of a resolving set of a graph was first introduced by Slater (1975) as a graph locating set, and by Harary and Melter (1976) independently as a graph resolving set. Furthermore, Chartrand et al. (1998) introduced a variant of a graph resolving set called a resolving partition of a graph. In this matter, the study focuses on finding the minimal partition of the vertex set of a graph G such that the representations of all vertices in G are different. In this case, representation of a vertex in G is determined by all its distance to all the partition classes. The study of a graph partition dimension has received much attention. As the first result, Chartrand et al. (1998) determined the partition dimension of some classes of trees, the double-star graphs and caterpillar graphs. Furthermore, Chartrand et al. (2000) characterized all graphs with order n-dimensional partition 2, n and n - 1 respectively.