Odd harmonious labeling of amalgamation of star graph
E Asumpta(1), Purwanto(1*), T D Chandra(1*)

(1)Departemen Matematika, Universitas Negeri Malang, Jalan Semarang 5, Malang 65145, Indonesia
*purwanto.fmipa[at]um.ac.id, tdanielchandra[at]gmail.com

Abstract

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 show that the amalgamation graphs S(C_4,n,r) is odd harmonious.

Keywords: odd harmonious, amalgamation, star graph

Topic: Mathematics