Let G(V, E) be a graph with order p and size q. The graph G is called as an even-odd harmonious graph if there exists an 1-1 map f:V → {1, 3, 5, …, 2p − 1} and a bijective map f∗:E → {0, 2, …, 2(q − 1)} such that f∗(e = uv) = (f(u) + f(v))(mod 2q). This computation of assigning the numbers to the vertices and edges of G is called an even-odd harmonious labeling of G. This article shows the existence of this labeling to certain family of graphs obtained through graph operations viz., i) Union of graphs ii) Superimposing and iii) Corona.
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