On the partition dimension of edge corona product of path and cycle

Abstract

Let v be a vertex of a connected graph G(V, E). Let S be a subset of V (G). For an ordered partition of V (G), the representation of a vertex with respect to is the k-vectors , where d(v, Sk ) represents the distance between the vertex v and the set Sk , defined by . The partition of V (G) is a resolving partition set if the k-vektors are distinct. The minimum resolving partition is a partition dimension of G, denoted by pd(G). The edge corona of G 1 and G 2 is defined as the graph obtained by taking one copy of G 1 and copies of G 2 and then joining two end-vertices of the i-th edge of G 1 to every vertex in the i-th copy of G 2. In this paper, we will study the partition dimension of the edge corona of cycle and path, namely and for n ≤ 2 and m ≤ 3.