Abstract
Cahit and Yilmaz [15] called a graph G is E-k - cordial if it is possible to label its edges with numbers from the set {0,1,...,k - 1} in such a way that, at each vertex nu of G, the sum modulo k of the labels on the edges incident with nu satisfies the inequalities vertical bar m(i) - m(j)vertical bar <= 1 and vertical bar n(i) - n(j)vertical bar <= 1, where m(S) and n(t) are, respectively, the number of edges labeled with s and the number of vertices labeled with t. In this paper, we give a necessary condition for a graph to be E-k - cordial for certain k. We also give some new families of E-k - cordial graphs and we prove Lee's conjecture about the edge-gracefulness of the disjoint union of two cycles.