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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

JEYANTHI, P; KALAIYARASI, R; RAMYA, D  and  SARATHA DEVI, T. Some results on skolem odd difference mean labeling. Proyecciones (Antofagasta) [online]. 2016, vol.35, n.4, pp.405-415. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172016000400004.

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.

Keywords : 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.

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