k-Product Cordial Labeling of Path Graphs

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 uv assign the label f( u )f( v )( modk ) . 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.