Abstract
Let f be a map from V (G) to {0, 1,..., k - 1}, where k is an integer and 1 <= k <= |V (G)|. For each edge uv assign the label f(u)f(v)(mod k). f is called a k-product cordial labeling if |v f (i) - v f (j)| <= 1, and |e f (i) - e f (j)| <= 1, i, j is an element of{0, 1,..., k - 1}, where vf (x) and ef (x) denote the number of vertices and edges, respectively labeled with x (x = 0, 1,..., k - 1). In this paper, we add some new results on k-product cordial labeling and prove that the graph P-n(2) is 4-product cordial. Further, we study the k-product cordial behaviour of powers of paths P-n(3), P-n(4) and P-n(5) for k = 3 and 4.