Open Neighborhood Coloring of Prisms

Geetha Kempanapura Nanjunda Swamy¹, Kyathsandra Nagendra Rao Meera^1*, Narahari Narasimha Swamy² & Badekara Sooryanarayana<sup>3


1</sup>Department 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.