Some results on skolem odd difference mean labeling

P. Jeyanthi, R. Kalaiyarasi, D. Ramya, T. Saratha Devi

Resumen


Let G = (V, E) be a graph with p vertices and q edges. A graph G is said to be skolem odd difference mean if there exists a function f : V(G) → {0, 1, 2, 3,...,p+3q — 3} satisfying f is 1-1 and the induced map f * : E(G) →{1, 3, 5,..., 2q-1} defined by f * (e) = [(f(u)-f(v))/2] is a bijection. A graph that admits skolem odd difference mean labeling is called skolem odd difference mean graph. We call a skolem odd difference mean labeling as skolem even vertex odd difference mean labeling if all vertex labels are even. A graph that admits skolem even vertex odd difference mean labeling is called skolem even vertex odd difference mean graph.

In this paper we prove that graphs B(m,n) : Pw, (PmõSn), mPn, mPn U tPs and mK 1,n U tK1,s admit skolem odd difference mean labeling. If G(p, q) is a skolem odd differences mean graph then p≥ q. Also, we prove that wheel, umbrella, Bn and Ln are not skolem odd difference mean graph.


Palabras clave


Skolem difference mean labeling; Skolem odd difference mean labeling; Skolem odd difference mean graph; Skolem even vertex odd difference mean labeling; Skolem even vertex odd difference mean graph; etiquetado de diferencia media de Skolem

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172016000400004

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