关于奇算术图

本文讨论了$n$个$m$长圈有一个公共结点图$C^n_m$, $n$个$m$长圈与$t$长路有一个公共结点图$C^n_m\cdot P_t$, $n$个$m$阶完全图有一个公共结点图$K^n_m$和星形图的同胚图的奇算术性问题.给出了完全图,完全二部图和圈是奇算术的充要条件.

On Odd Arithmetic Graphs

The following results are obtained: (1) The graph Cnm·Pt is odd arithmetic when (i)m =0 (mod 2) and t=m or m+1; (ii) m=1 (mod 2) and t=m+1. (2) The graph Cn2m is odd arithmetic when (i) m=2,4 and n is any positive integer; (ii) m=3 and n is even. (3) The graph Cnm is odd arithmetic when m=4n and t=-2. (4) Pnm+1 is odd arithmetic when (i) n is odd; (ii) m ≤ 3 and n is any positive integer. (5) Windmill graph Ktn is odd arithmetic if and only if n=2. (6) Cycle Cn is odd arithmetic if and only if n = 0 (mod 4). (7) For any positive integer n and any positive integer m, Km,n is odd arithmetic.