Abstract
Hovey [Discrete Math. 93 (1991), 183-194] introduced simultaneous generalizations of harmonious and cordial labellings. He defines a graph G of vertex set V (G) and edge set E(G) to be k-cordial if there is a vertex labelling f from V (G) to Zk, the group of integers modulo k, so that when each edge xy is assigned the label (f(x) + f(y)) (mod k), the number of vertices (respectively, edges) labelled with i and the number of vertices (respectively, edges) labelled with j differ by at most one for all i and j in Z(k). In this paper we give some necessary conditions for a graph to be k-cordial for certain k. We also give some new families of 4-cordial graphs.