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

A graph <em>G</em> with <em>q</em> edges is said to be odd harmonious if there exists an injection <em>f</em>:<em>V</em>(<em>G</em>) → ℤ_2q so that the induced function <em>f</em>*:<em>E</em>(<em>G</em>)→ {1,3,...,2<em>q</em>-1} defined by <em>f</em>*(<em>uv</em>)=<em>f</em>(<em>u</em>)+<em>f</em>(<em>v</em>) is a bijection.<p>Here we show that graphs constructed by edge comb product of path <em>P</em>_n and cycle on four vertices <em>C</em>₄ or shadow of cycle of order four <em>D</em>₂(<em>C</em>₄) are odd harmonious.</p>

Even-odd Harmonious Labeling of Some Graphs

Let G = be a graph, with and . An injective mapping is called an even-odd harmonious labeling of the graph G, if an induced edge mapping such that (i) is bijective mapping (ii) The graph acquired from this labeling is called even-odd harmonious graph. In this paper, we discovered some interesting results like H-graph, comb graph, bistar graph and graph for even-odd harmonious labeling.