Graph Operations and Cordiality

Abstract

In this paper, we show that the disjoint union of two cordial graphs, one of them is of even size, is cordial and the join of two cordial graphs, both are of even size or one of them is of even size and one of them is of even order, is cordial. We also show that \(C_m \cup C_n \) is cordial if and only if \(m+n \not\equiv 2 \pmod{4}\) and \(mC_n\) is cordial if and only if \(mn \not\equiv 2 \pmod{4}\) and for \(m, n \geq 3\), \(C_m + C_n\) is cordial if and only if \((m, n) \neq (3, 3)\) and \(\{m, n\} \not\equiv \{0, 2\} \pmod{4}\).

Finally, we discuss the cordiality of \(P_n^k\).