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In [1] Abdel-Aal has introduced the notions of m-shadow graphs and n-splitting graphs, for all m, n ≥ 1. In this paper, we prove that, the m-shadow graphs for paths and complete bipartite graphs are odd harmonious graphs for all m ≥ 1. Also, 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. In addition, we present some examples to illustrate the proposed theories. Moreover, we show that some families of graphs admit odd harmonious libeling.
Odd harmonious labeling, m-shadow graph, m-splitting graph, Odd harmonious labeling, m-shadow graph, m-splitting graph., Odd harmonious labeling
Odd harmonious labeling, m-shadow graph, m-splitting graph, Odd harmonious labeling, m-shadow graph, m-splitting graph., Odd harmonious labeling
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