关于图的邻和可区别全染色的新方法

A new method of neighbor sum distinguishing total coloring of graphs

给出树的邻和可区别2-全染色方案,并结合三正则图最小消圈集的独立性以及消圈子图的无圈性,较为简洁地证明三正则图的邻和可区别全色数满足1-2猜想。进一步利用独立消圈集法确定r-正则图、Halin图以及路与路的笛卡尔乘积图的邻和可区别全色数。

The neighbor sum distinguishing 2-total coloring of a tree is presented along with the independence of the minimum decycling set of a 3-regular graph and the acyclicity of the corresponding decycling subgraphs.This method provides a simple way to prove that the neighbor sum distinguishing total chromatic number of a 3-regular graph satisfies the 1-2 Conjecture.The independent decycling set method is used to determine the neighbor sum distinguishing total chromatic number of an r-regular graph,Halin graph,and Cartesian product graph of paths.