Harmonious labeling on some join and Cartesian product of graphs.

LetG = (V, E) be a simple and undirected graph with |V| vertices and |E| edges. Consider a graph G with |E| ≥ |V|. An injective f from V to a set {0,1,2,... , |E|−1} such that the induced edge labeling given by f(xy) = g(x) + g(y) (mod |E|) for any edge xy in the graph is also an injective function, is called harmonious labeling of a graph G. A harmonious graph is a graph which has a harmonious labeling. In this paper we show an existence of harmonious labeling on G + K ¯ 2 and G × P2, where G is a harmonious unicyclic graph. [ABSTRACT FROM AUTHOR]