Odd Harmonious Labeling of Pn ⊵ C4 and Pn ⊵ D2(C4)

Abstract

A graph G with q edges is said to be odd harmonious if there exists an injection f:V(G) → ℤ_2q so that the induced function f*:E(G)→ {1,3,...,2q-1} defined by f*(uv)=f(u)+f(v) is a bijection.

Here we show that graphs constructed by edge comb product of path P_n and cycle on four vertices C₄ or shadow of cycle of order four D₂(C₄) are odd harmonious.