%0 Journal Article
%T <i>d-Distance</i> Coloring of Generalized Petersen Graphs <i>P(n, k)</i>
%A Ramy Shaheen
%A Ziad Kanaya
%A Samar Jakhlab
%J Open Journal of Discrete Mathematics
%P 185-199
%@ 2161-7643
%D 2017
%I Scientific Research Publishing
%R 10.4236/ojdm.2017.74017
%X A coloring <img src=\"Edit_f10de6cf-16b2-4c5e-83a0-f60130a9472d.bmp\" alt=\"\" /> of <em>G</em> is <em>d-distance</em> if any two vertices at distance at most d from each other get different colors. The minimum number of colors in <em>d-distance</em> colorings of <em>G</em> is its <em>d-distance</em> <em>chromatic number</em>, denoted by<em> ¦Ö</em><sub><em>d</em></sub>(<em>G</em>). In this paper, we give the exact value of <em style=\"white-space:normal;\">¦Ö</em><sub style=\"white-space:normal;\"><em>d</em></sub><span style=\"white-space:normal;\">(</span><em style=\"white-space:normal;\">G</em><span style=\"white-space:normal;\">)</span> (d = 1, 2), for some types of generalized Petersen graphs <em>P</em>(<em>n, k</em>) where k = 1, 2, 3 and arbitrary <em>n</em>.
%K Distance Coloring
%K Generalized Petersen Graphs
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=79024