\(E\)-cordial Graphs

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 \(f(v) = \sum_{\forall u} f(u,v) \pmod{2}\), where \(v \in V\) and \(\{u,v\} \in E\), so that the conditions \( |v_f(0)| – |v_f(1)| \leq 1\) and \(\big| |e_f(0)| – |e_f(1)| \leq 1\) are satisfied, where \(|v_f(i)|\) and \(|e_f(i)|\), \(i = 0,1\), 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 labeling. In this paper, we investigate \(E\)-cordiality of several families of graphs, such as complete bipartite graphs, complete graphs, wheels, etc.