Open Journal of Discrete Mathematics

Volume 7, Issue 4 (October 2017)

ISSN Print: 2161-7635   ISSN Online: 2161-7643

Google-based Impact Factor: 0.48  Citations  

d-Distance Coloring of Generalized Petersen Graphs P(n, k)

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DOI: 10.4236/ojdm.2017.74017    1,153 Downloads   2,233 Views  Citations

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.

Share and Cite:

Shaheen, R. , Kanaya, Z. and Jakhlab, S. (2017) d-Distance Coloring of Generalized Petersen Graphs P(n, k). Open Journal of Discrete Mathematics, 7, 185-199. doi: 10.4236/ojdm.2017.74017.

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