奇围长为r的对称图的指数集

THE EXPONENT SET OF SYMMETRIC DIGRAPH WITH ODD GIRTH R

令E_(r,n) 表示夸围长为r的n阶对称图的指数集。本文证明了:E_(1,n)={1,2,…,2n-2}\x_1,当3≤r≤n时,E_(r,n)={r一1,r,…,2n-r-1}\x_r 其中x_i为[2[n\2]-i+2,2n-i-1]中的奇数,i=1,r.并刻划了指数为2n-r-1的奇围长为r的对称图的特征。

Let Ern be the exponent set of symmetric digraph with odd girth r and order n. In this paper, we show that E 1,x = {1,2,…,2n - 2}\x 1 . Ern ={r - 1, r,…, 2n - r- 1}\xr as 3≤ r ≤ n where .x,- is the set of odd numbers in [2[a/2] - i + 2, 2n - i - 1](i= 1, r). Furthermore, we also describe a characterization of the symmetric digraph with odd girth r whose exponent is equal to 2n-r-1.