Open neighborhood coloring of prisms

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.