蛛形图的全图和中心图的均匀染色

The equitable chromatic number of the total graph and central graph of a spider

通过研究蛛形图的全图和中心图的性质,给出具体的独立集分法,得到了蛛形图G删去头点后有n条长为n-1的路.把图G的全图记为T(G),则G的全图的均匀色数χEq[T(G)]=n+1.把G的中心图记为C(G),也得到了这样的蛛形图G的中心图的均匀色数:当n=2k时χ,Eq[C(G)]=2k2+1;当n=2k+1时,χEq[C(G)]=2k2+3k+1.

The property of the total graph and central graph of a spider were discussed,by giving the certain in dependent set,it was proved that if graph G was a spider then it contained n paths with the length of n-1 after removing the head.Let T（G） denote the total graph of G,then the equitable chromatic number of the total graph of GχEq=n＋1.Let C（G） denote the central graph of G,the equitable chromatic number of the central graph of G was also obtained： χEq =2k^2＋1 when n=2k,χEq=2k^2＋3k＋1 when n=2k＋1.