Right Type Departmental Bulletin Paper

A graph $\Gamma $ with diameter $d $ is said to be distance-regular if there are integers bi $(\mathrm{i}=$ $0 $ , $\cdots $ , $d- $ $1 $ ) and $c_{i}(\mathrm{i}=1, \cdots, d) $ such that for any two veritices $x $ and $y $ such that $d(x, y)=\mathrm{i} $, $b_{i} $ $=\# $ {$z|z $:vertex, $d $ ( $x $ , $z)=i+1 $ , $d(y, $ $z)=1 $}