### 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,v**Î**V(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,S*

_{1}), d(v,S_{2})_{, }d(v,S_{3}), ..., 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. *

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