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An assignment of integers to vertices or edges of a graph subject to certain conditions is called graph labeling. One of the various of graph labeling is an odd harmonious labeling. Let G be a graph having q edges. An odd harmonious labeling of G is an injective function f from the set of vertices of G to the set {0, 1, 2,,... , 2q - 1} such that the induced function f*, where f*(uv)=f(u)+f(v) for every edge uv of G, is a bijection from the set of edges of G to {1, 3, 5,..., 2q - 1}. If a such labeling exists, then G is said to be odd harmonious. In this paper we study harmonious labeling of amalgamation graph (C4, n, r). First, we define an injective function f from the set of vertices of (C4, n, r) to the set {0, 1, 2, ,..., 2q - 1}, and then show that the induced function function f* is bijective. We find that the amalgamation graph (C4, n, r) is odd harmonious. [ABSTRACT FROM AUTHOR]

Graph labeling is a way of assigning integers to vertices or edges of a graph that satisfy certain conditions. One of graph labeling is odd harmonious labeling. Let G = G(p, q) be a graph that have p vertices and q edges. An odd harmonious labeling of G is an injective function f from the set of vertices of G to the set { 0, 1, 2, ..., 2q - 1} such that the induced function f*, where f*: E(G) → {1, 3, 5, ... , 2q - 1}, and f* (uv) = f(u) + f(v) for every edge uv ∈ E(G), is bijective. A snake graph k(G) is a graph obtained from a path on k edges by replacing each edge by a graph isomorphic to G. If such labeling exists, then G is said to be odd harmonious. In this paper we show that snake graph k(G) is odd harmonious for some graph G. [ABSTRACT FROM AUTHOR]