The odd harmonious labeling of matting graph

Abstract

Let G(p, q) be a graph that consists of p vertices and q edges, where V is the set of vertices and E is the set of edges of G. A graph G(p, q) is odd harmonious if there exists an injective function f that labels the vertices of G by integer from 0 to 2q − 1 that induced a bijective function f ∗ defined by f ∗(uν) = f(u) + f(ν) such that the labels of edges are odd integer from 1 to 2q − 1. A graph that admits harmonious labeling is called a harmonious graph. A matting graph is a chain of C 4 −snake graph. A matting graph can be view as a variation of the grid graph. In this paper, we prove that the matting graph is an odd harmonious graph.