Open Neighborhood Coloring of Prisms

For a simple, connected, undirected graph G(V, E) an open neighborhood coloring of the graph G is a mapping f : V (G) --> Z+ such that for each w in V(G), and for all u, v in N(w), f(u) is different from f(v). The maximum value of f(w), for all w in V (G) is called the span of the open neighborhood coloring f. The minimum value of span of f over all open neighborhood colorings f is called open neighborhood chromatic number of G, denoted by Xonc(G). In this paper we determine the open neighborhood chromatic number of prisms