Partition Dimention of Amalgamation-Side in Cycle Graph

Abstract

The graph is a pair of sets , where is a finite set whose elements are called vertices, and is the set of pairs of members of . which is called the edge. Let be a simple graph where . The distance between points and is denoted by is the length of the shortest path between and . Given and there is a vertex on the connected graph , then the distance between and is denoted . If is -partition of , then the representation of with respect to is -ordered pairs, . If the -ordered pairs for are all different, then the partition is called a dimension partition. The minimal -number which is the -differentiating partition of is called the partition dimension of and is denoted by . In this study, the partition dimensions of the sided amalgamation result will be determined on an even-order cycle graph. In determining the dimensions of the partition, characterization of the partition dimensions is used in the path graph, the lemma about the distinguishing set and the equivalence point, especially in the even-order cycle graph. The results of this study are pd(Amal(Cn,e,k)) = 3 for n≥4 , pd(Amal(C4,e,k))=4 for k=4 , pd(Amal(C4,e,k))=3+m for k=2m+3 and k=2m+4 where m=1,2,3,...