Odd Harmonious Labeling of <em>P</em>_n ⊵ <em>C</em>₄and&nbsp; <em>P</em>_n ⊵ <em>D</em>₂(<em>C</em>₄)

Abstract

A graph G with q edges is said to be odd harmonious if there exists an injection f:V(G) → ℤ2q 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 Pn and cycle on four vertices C4 or shadow of cycle of order four D2(C4) are odd harmonious.

Keywords

• odd harmonious labeling
• edge comb product
• path
• cycle
• shadow graph.