Odd harmonious labeling of super subdivisión graphs

Abstract

A graph G(p, q) is said to be odd harmonious if there exists an injection ????: V (G) → {0, 1, 2, · · · , 2q − 1} such that the induced function ????∗ : E(G) → {1, 3, · · · , 2q − 1} defined by ????∗(uv) = ???? (u) + ???? (v) is a bijection. In this paper we prove that super subdivision of any cycle Cm with m ≥ 3 ,ladder, cycle Cn for n ≡ 0(mod 4) with K1,m and uniform fire cracker are odd harmonious graphs.