途径正则有向图的途径正则不变性

The Walk-regular Invariability of Walk-regular Digraphs

给出了途径正则有向图的概念,利用矩阵理论、谱理论给出了途径正则有向图的补图、2个途径正则有向图的字典式积与直积都是途径正则的.此外,还定义了有向图的完全正则划分,证明了完全正则Seidel-switching不改变有向图的途径正则性.

The lexicographic product and the direct product of walk-regular digraphs are all walk-regular by matrix theory and spectrum theory.Furthermore,the complete regular partition is defined,and it is showed that the complete regular Seidel-switching doesn＇t change the walk-regular property.