循环图C_n〈j_1,j_2,…,j_r,n/2〉的连通性

Connectedness for Circulant Graph C_n<j_1,j_2,…,j_r,n/2>

本文得到了奇数度循环图C_n<j_1,j_2,…,j_r,n/2>是连通的充要条件及C_n<j_1,j_2,…,j_r,n/2)×K_2(j_r≠n/2)为循环度的充要条件,并进一步研究了C_n<j_1,j_2,…,j_r,n/2>不连通的情形.证明了三度连通循环图C_n<j,n/2>同构于C_n<1,n/2>或C_n<2,n/2>.这一结果颇有意义.

In this paper, the necessary and sufficient condition for odd degree circulant graph C_n<j_1, j_2,…,j_r,n/2> being connected is derived, and the necessary and sufficient condition for C_n<j_1, j_2,…,j_r>×K_2(j_r≠n/2) being a circulant graph is obtained. The cases for circulant graph C_n (j_1,j_2,…,n/2> being disconnected are discussed. Three degree connected circulant graph C_n<j,n/2> being isomorphic with C_n<1,m/2> or C_n<2,n/2> is proved.