In this paper, we prove that the graphs \(P_n\) (\(n \geq 3\)), \(C_n\) (\(n \geq 3\), \(n \not\equiv 4 \pmod{8}\)), and \(K_n\) (\(n \geq 3\)) are \(E_4\)-cordial graphs. Additionally, we show that every graph of \(\geq 3\) is a subgraph of an \(E_4\)-cordial graph.