TY - JOUR AU - Jeyanthi, P. AU - Kalaiyarasi, R. AU - Ramya, D. AU - Devi, T. Saratha PY - 2017/03/23 Y2 - 2024/03/28 TI - Some results on skolem odd difference mean labeling JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 35 IS - 4 SE - DO - 10.4067/S0716-09172016000400004 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1318 SP - 405-415 AB - <p style="font-size: 13.192px; font-family: verdana, arial;" align="justify"><span style="font-family: verdana; font-size: x-small;">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.</span></p><p style="font-size: 13.192px; font-family: verdana, arial;" align="justify"><span style="font-family: verdana; font-size: x-small;">In this paper we prove that graphs B(m,n) : P<sub>w</sub>, (P<sub>m</sub>õS<sub>n</sub>), mP<sub>n</sub>, mP<sub>n</sub> U tP<sub>s</sub> and mK <sub>1,n</sub> U tK<sub>1,s</sub> 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, B<sub>n</sub> and L<sub>n</sub> are not skolem odd difference mean graph.</span></p> ER -