APPLICATION OF ODD HARMONIOUS LABELLING OF GRAPHS

The labelling of discrete structures is an attractive research topic due to its vast range of applications. The current research is looking on strange harmonious labelling. If there exists an onto ff:V(G)→{0,1,2,,2q−1} such that the induced function ∗:E(G) →{1,3, ,2q−1}defined by f (uv) = f(u) + f(v) is a bijection, the graph G is said to be odd harmonious. We discuss a variety of graphs with unusually synchronized labelling. As we show, Bistar Bn, shadow n's graph, and splitting graph are all odd harmonic graphs. We also show that the random super subdivision of path Pn allows for odd harmonious labelling. We further prove that for n =0(mod 4) the graph H(n,n) and the joint sum of two copies of cycle Cn are odd harmonic graphs