In this paper, we prove that the cycle \(C_n\) with parallel chords and the cycle \(C_n\) with parallel \(P_k\)-chords are cordial for any odd positive integer \(k \geq 3\) and for all \(n \geq 4\) except for \(n \equiv 4r + 2, r \geq 1\). Further, we show that every even-multiple subdivision of any graph \(G\) is cordial and we show that every graph is a subgraph of a cordial graph.