E-cordial graphs

Abstract

A graph G = (V,E) is called E-cordial if it is possible to label the edges with the numbers from the set N = (0,1) and the induced vertex labels f(v) are computed by f(v) = Sigma(For All u)f(u,v) (mod 2), where v is an element of V and (u,v) is an element of E so that the conditions \ v(f)(0) - v(f)(1) \ 1 and \ e(f)(0) - e(f)(1) \ less than or equal to 1 are satisfied, where v(f)(i) nnd e(f)(i),i = 0,1 denote the number of vertices and edges labeled with 0's and 1's, respectively. The graph G is called E-cordial if it admits an E-cordial labelling. In this paper we investigate E-cordiality of several families of graphs such as complete bipartite graphs, complete graphs, wheels, etc.