Abstract
Further Results on Odd Harmonious Graphs
Highlights
We begin with simple, finite, connected and undirected graph G = (V, E) with p vertices and q edges
We prove that, the m-shadow graphs for paths and complete bipartite graphs are odd harmonious graphs for all m ≥ 1
We prove the n-splitting graphs for paths, stars and symmetric product between paths and null graphs are odd harmonious graphs for all n ≥ 1
Summary
For any integers m ≥ 1, the m-shadow graph denoted by Dm (G) and the m- splitting graph denoted by Splm(G) are defined as follows: Definition 1.1. Further they prove that the splitting graphs of the path Pn and the star K1,n admit odd harmonious labeling. We prove that, the following graphs Splm( Pn ), Splm( K1,n ), Pn ⊕ Km , Splm (Pn ⊕ K 2 ), Splm(P2 ∧ Sn), Spl (Km,n ) are odd harmonious.
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