Graph operations and cordiality

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 Cm∪ Cn is cordial if and only if m+n ≡/ 2 (mod 4) and mCn is cordial if and only if mn ≡/ 2 (mod 4) and for m, n ≥ 3, Cm + Cn is cordial if and only if (m, n) ≠ (3, 3) and {m,n} ≡/ {0, 2} (mod 4). Finally, we discuss the cordiality of k n P . 1-Introduction All graphs in this paper are finite, simple and undirected. We follow the basic notations and terminology of graph theory as in [5]. Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) → {0, 1induces an edge labeling f*:E(G) →{0, 1}, defined by f*(xy) = |f(x) − f(y)|, for each edge xy ∈ E(G). For i ∈ {0, 1}, let ni(f) =| {v ∈ V(G) : f(v) = i}| and mi(f) = |{e ∈ E(G) : f*(e) = i}|.A labeling f of a graph G is cordial if | n0(f) − n1(f) | ≤ 1 and | m0(f) − m1(f) | ≤ 1. Note that interchanging the vertex labels 0 and 1 will produce a new cordial labeling of G. So that we may always assume that there is a cordial labeling f with the additional property 0 ≤ n0(f) − n1(f) ≤ 1 or − 1 ≤ n0(f) − n1(f) ≤ 0 . A graph G is cordial if it admits a cordial labeling. The notion of cordial labeling of graphs was first introduced by Cahit