k-途径正则有向图

The Bessel Numbers and Bessel Matrices

中文关键词:  $k$-途径正则有向图  预距离多项式, 交叉$uv$-局部重数.

英文关键词:$k$-walk-regular digraph  predistance polynomial  the crossed $uv$-local multiplicity.

中文摘要:

      本文定义了$k$-途径正则有向图, 研究了这类图的性质,给出了这类图的一些代数刻画, 并指出当$k=0$时, 该类图便是文献[5]中刘稳等定义的途径正则有向图, 而$k=D$时, 该类图便是文献[2]中由F.Comellas等定义的弱距离正则有向图.

英文摘要:

      In this paper, we define a class of strongly connected digraph, called the $k$-walk-regular digraph, study some properties of it, provide its some algebraic characterization and point out that the $0$-walk-regular digraph is the same as the walk-regular digraph discussed by Liu and Lin in 2010 and the $D$-walk-regular digraph is identical with the weakly distance-regular digraph defined by Comellas et al in 2004.