Distance Coloring Of Special Classes Of Graphs

The initial form of the distance coloring of graphs was introduced byF.Kramer and H.Kramer in[2, 3] at first. It was defined the distance col-oring of graphs by T.R.Jensen and B.Toft in [18]latter. For a positiveinteger k, a k-distance coloring of graph G is an assignment of k colors{1,2,3,···,n} to the vertices of G such that any two vertices of G of dis-tance not greater than k have distinct colors. The k-distance chromaticnumber of G,χk(G), is the minimum number of colors in a k-distance col-oring of G. In this thesis, we study the k-distance coloring of some specialclasses of graphs,our paper have four sections:1.We introduce the concepts and the lemmas associating with the k-distance coloring of graphs.2. We obtain the k-distance chromatic number of Mycielski graphs ofsome special classes of graphs.3. We study the 2-distance coloring of weak product graphs of some spe-cial classes of graphs,and obtain the approachable boundary of 2-distancechromatic number of weak product graphs,we give the 2-distance chromaticnumber of weak product graphs of some special classes of graphs.4.We give the 2-distance chromatic number of monocycle graphs.