k-Product Cordial Labeling of Path Graphs

Abstract

In 2012, Ponraj et al . defined a concept of k-product cordial labeling as follows: Let f be a map from V ( G ) to { 0,1, ⋯ , k − 1 } where k is an integer, 1 ≤ k ≤ | V ( G ) | . For each edge u v 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 ∈ { 0,1, ⋯ , k − 1 } , where v f ( x ) and e f ( x ) denote the number of vertices and edges respectively labeled with x ( x = 0,1, ⋯ , k − 1 ). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs P n admit k-product cordial labeling.