The Bridge Graphs Partition Dimension

Abstract

Finding the partition dimension of graph is still an open problem in the graph theory. Therefore, several researchers investigate the problem in several operations of the graph. For example, the partition dimension of corona product, cartesian product, subdivision operation has been published by several researchers. Let G1, G2 be two connected graphs. We present the partition dimension of a graph G which is obtained from two graphs G1( G2 with a linking a vertex in G1 to one vertex in G2 (a bridge in graph G). This paper is devoted to find the upper bound of partition dimension of the connected two graphs by a bridge.