Odd Harmonious Labeling of Some New Families of Graphs

A graph G(p, q) is said to be odd harmonious if there exists an injection f : V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function f∗ : E(G) → {1, 3, · · · , 2q − 1} defined by f∗(uv) = f(u) + f(v) is a bijection. A graph that admits odd harmonious labeling is called odd harmonious graph. In this paper, we prove that shadow and splitting of graph K2,n, Cn for n ≡ 0 (mod 4), the graph Hn,n, double quadrilateral snakes DQ(n), n ≥ 2, the graph Pr,m if m is odd, banana tree and the path union of cycles Cn for n ≡ 0 (mod 4) are odd harmonious. AMS 2010 Mathematics Subject Classification. 05C78.