TITLE:
d-Distance Coloring of Generalized Petersen Graphs P(n, k)
AUTHORS:
Ramy Shaheen, Ziad Kanaya, Samar Jakhlab
KEYWORDS:
Distance Coloring, Generalized Petersen Graphs
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.7 No.4,
September
13,
2017
ABSTRACT: A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χd(G). In this paper, we give the exact value of χd(G) (d = 1, 2), for some types of generalized Petersen graphs P(n, k) where k = 1, 2, 3 and arbitrary n.