# Some results on skolem odd difference mean labeling

• P. Jeyanthi Govindammal Aditanar College for Women.
• R. Kalaiyarasi Dr. Sivanthi Aditanar College of Engineering.
• D. Ramya Government Arts College for Women.
• T. Saratha Devi G. Venkataswamy Naidu College.
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

### 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.

### Biografía del autor

P. Jeyanthi, Govindammal Aditanar College for Women.
Research Centre, Department of Mathematics.
R. Kalaiyarasi, Dr. Sivanthi Aditanar College of Engineering.
Department of Mathematics.
D. Ramya, Government Arts College for Women.
Department of Mathematics.
T. Saratha Devi, G. Venkataswamy Naidu College.
Department of Mathematics.

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