Open neighborhood coloring of graphs
Geetha K. N., K. N. Meera, N. Narahari, B. Sooryanarayana · International Journal of Contemporary Mathematical Sciences · 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 ∈ V , and ∀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 value of span of f over all open neighborhood colorings f is called open neighborhood chromatic number of G, denoted by χonc(G). In this paper we determine the open neighborhood chromatic number of some standard graphs, trees and the infinite triangular lattice. 676 Geetha K. N., K. N. Meera, Narahari N. and B. Sooryanarayana Mathematics Subject Classification: 05C15