Some Problems in Cordial Labelings of Graphs

In a seminal paper in 1987, I. Cahit introduced cordial labelings. We take G to be a finite, simple, undirected graph with vertex set V and edge set E. Let f be a surjection from the vertex set V to the set {0,1}. This function induces an edge labeling |f(u)-f(v)| to each edge uv of the graph G. Let v_f (0), v_f (1) denote respectively the number of vertices in G labeled 0 and 1 by f. Let e_f (0), e_f (1) denote respectively the number of edges in G labeled 0 and 1. Then f is called a cordial labeling of G if |v_f (0)- v_f (1)|¿1 and |e_f (0)-e_f (1) |¿. A graph G is said to be cordial if it has a cordial labeling. I. Cahit proved that every tree is cordial, all fans are cordial; an Eulerian graph is not cordial if the number of edges e is congruent to 2(mod 4). In this book, we have investigated the cordiality of various types of graphs viz. Corona graphs, t-ply graphs, elongated plys and some wheel related graphs.