Open neighborhood coloring of prisms

Abstract

For a simple, connected, undirected graph G(V, E), an open neighbor-hood coloring of the graph G is a mapping f: V(G) → Z+, such that for each w∈ V and V∀ u, v∈ N(w), f (u) ≠ f (v). The maximum value of f (w), ∀w∈V (G) is called the span of the open neighborhood coloring f. The minimum span of f over all the open neighborhood colorings f is called the open neighborhood chromatic number of G, denoted by χoac (G). In this paper, we determine the open neighborhood chromatic number of prism graph which is a generalized Petersen graph GP(n, k) for n ≥ 3 and k = 1. © 2013 Published by ITB Journal Publisher.