%0 Journal Article
%T On the Maximum Number of Dominating Classes in Graph Coloring
%A Bing Zhou
%J Open Journal of Discrete Mathematics
%P 70-73
%@ 2161-7643
%D 2016
%I Scientific Research Publishing
%R 10.4236/ojdm.2016.62006
%X We investigate
the dominating-<i><span style=\"font-family:Symbol;\">c</span></i><span>-color number,<img src=\"Edit_4cdfb2db-b361-464c-82f6-e37499c36f1c.bmp\" alt=\"\" /></span><span>, of a
graph <i>G</i>. That is the maximum number
of color classes that are also dominating when <i>G</i> is colored using</span><span> <img src=\"Edit_e5a0ff00-eb3f-41be-892e-b23fab35c57c.bmp\" alt=\"\" /> colors. We show that <img src=\"Edit_860c3b30-eb4f-4697-998e-98a390277c78.bmp\" alt=\"\" /></span><span> where <img src=\"Edit_0ac0a0ec-221c-4c42-91c1-8314511ef108.bmp\" alt=\"\" /></span><span> is the join of <i>G</i> and <img src=\"Edit_082e927b-6141-4c77-96e6-bfe57a6530c8.bmp\" alt=\"\" /></span><span>. This
result allows us to construct classes of graphs such that <img src=\"Edit_db7872bd-d208-485e-8e79-979bae33bf98.bmp\" alt=\"\" /></span><span> and <img src=\"Edit_6d7606a7-fe01-46ca-8091-680c5c5c4693.bmp\" alt=\"\" /></span><span> thus provide some information regarding two
questions raised in [1] and [2].</span>
%K Graph Coloring
%K Dominating Sets
%K Dominating Coloring Classes
%K Chromatic Number
%K Dominating Color Number
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=65335