Emiliana Asumpta, Purwanto, Tjang D. Chandra
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. © 2022 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, Universitas Negeri Malang, Jl. Semarang 5, Malang, 65145, Indonesia