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Open Neighborhood Coloring of Prisms
Geetha Kempanapura Nanjunda Swamy1, Kyathsandra Nagendra Rao Meera1*, Narahari Narasimha Swamy2 & Badekara Sooryanarayana3
1Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bangalore, Karnataka State, INDIA, 560 035
2Department of Mathematics, University College of Science, Tumkur University, Tumkur, Karnataka State, INDIA, 572 103
3Department of Mathematical and Computational Studies, Dr. Ambedkar Institute of Technology, Bangalore, Karnataka State, INDIA, 560 056
Email: kn_meera@blr.amrita.edu
Abstract. 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.
Keywords: coloring; labeling; neighbor; open neighborhood; prism.
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