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 τ : V (G) → Z2q so that the induced function τ ∗ : E(G) → {1, 3, . . . , 2q − 1} defined by τ ∗ (xy) = τ (x) + τ (y) is a bijection. Here we show that graphs constructed by edge comb product of path Pn and cycle on four vertices C4 or shadow of a cycle of order four D2(C4) are odd harmonious.