DIAMETER DAN DIMENSI PARTISI PADA GRAF CATERPILLARS

Abstract

Suppose G=(V,E) is connected graph and u,v Î V are any two points in G . Diameter G is defined as the maximum distance between two points in G, denoted by diam (G) = max{d(u,v)|u,vÎV(G)}. Diameter of Caterpillars Graph (C_n,m) is diam(C_n,m) = n + 1. Suppose there is a point v in G. Then the representation v to P is defined as r(v|P = (d(v,S₁), d(v,S₂)_, d(v,S₃), ..., d(v,S_k)). If any different point in G has a different representation of the P, then P is called the resolving partition. The minimum cardinality of k-resolving partition against V(G) referred to the partition dimension of G, denoted by pd(G). Partition dimension of graph Caterpillars (C_n,m) is pd(C_n,m) = n.m + 1

Key Words: Caterpillars Graph, Diameter Graph, Partition Dimension, Resolving Partition.