Open Neighborhood Coloring of Prisms

Geetha Kempanapura Nanjunda Swamy (Department of Mathematics, Amrita School of Engineering)
Kyathsandra Nagendra Rao Meera (Department of Mathematics, Amrita School of Engineering)
Narahari Narasimha Swamy (Department of Mathematics, University College of Science, Tumkur University)
Badekara Sooryanarayana (Department of Mathematical and Computational Studies, Dr. Ambedkar Institute of Technology)

Journal of Mathematical and Fundamental Sciences
Vol. 45 No. 3 (2013)

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.