The odd harmonious labelling of n hair-kC4-snake graph

Abstract

Let G(p, q) be graph that consists of p = |V} vertices and q = |E| 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 exist an injective function f:V → {0,1,2,...,2q - 1} that induced a bijective function f*:E → {1, 3, 5,...,2q - 1} defined by f* (uv) - f(u) + f(v). The function / is called harmonious labelling of graph G(p, q). A hair-kC4 snake graph is a graph obtain by attaching n leaves to vertices of degree two in kC4-snake graph. In this paper we prove that nhair-kC4-snake graph is odd harmonious.