Odd Harmonious Labelings of Cyclic Snakes

In [8] Liang and Bai have shown that the kC₄ − snake graph is an odd harmonious graph for each k ≥ 1. In this paper we generalize this result on cycles by showing that the kC_n − snake with string 1,1,…,1 when n ≡ 0 (mod 4) are odd harmonious graph. Also we show that the kC₄ − snake with m-pendant edges for each k,m ≥ 1 , (for linear case and for general case). Moreover, we show that, all subdivision of 2 m∆_k - snake are odd harmonious for each k,m ≥ 1 . Finally we present some examples to illustrate the proposed theories.