路的3类积图的邻点扩展和可区别全染色

Neighbor Expanded Sum and Distinguishing Total Coloring of Three Kinds of the Product Graphs of Paths

【目的】为了得到两条路的积图的邻点扩展和可区别全色数。【方法】直接构造了两路的笛卡尔积、直积、半强积的邻点扩展和可区别全染色。【结果】得到这3类积图的邻点扩展和可区别全色数。【结论】证明了NESDTC猜想对于两路的笛卡尔积、直积、半强积成立。

[Purposes]To obtain the neighbor expanded sum and distinguishing total chromatic number of product graph of two paths.[Methods]The neighbor expanded sum and distinguishing total coloring of product graphs are constructed,such as the Cartesian product,direct product and semi-strong product.[Findings]The neighbor expanded sum and distinguishing total chromatic number of two paths are given.[Conclusions]NESDTC conjecture is true for the product graphs of paths.