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Odd harmonious labeling of super subdivisión graphs. (English) Zbl 1442.05196

Summary: A graph \(G(p, q)\) is said to be odd harmonious if there exists an injection \( f : V (G) \rightarrow \{0, 1, 2, \dots, 2q- 1\}\) such that the induced function \(f^\ast : E(G) \rightarrow \{1, 3, \dots, 2q-1\}\) defined by \(f^\ast (uv) = f (u) + f(v)\) is a bijection. In this paper we prove that super subdivision of any cycle \(C_m\) with \( m \geq 3\), ladder, cycle \(C_n\) for \(n \equiv 0\pmod 4\) with \(K_{1,m}\) and uniform fire cracker are odd harmonious graphs.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
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