任意k紧优双环网络无限族的构造

在L形瓦理论的基础上,结合中国剩余定理和数论中的素数理论,通过讨论A+z-2j≠0的一般情况,证明可以构造任意k_0紧优双环网络无限族:{N(t)=3t~2+(2i-1)t+B;B=k_0~2-nk_0+m,t=f~2-if-nk_0+m,f=(2i-i~2+4B)p_1~2p_2~2…p_(k_0~2)~2e+c,其中i=1,3,e≥0,m,n均为整数}.结点数N(t)为e的4次多项式,也可以为e的2次多项式且系数含有参数.

THE CONSTRUCTION OF INFINITE FAMILIES OF k-TIGHT OPTIMAL DOUBLE LOOP NETWORKS

Based on the theory of $L$-shaped tile, Chinese remainder theorem and prime number theory, it is proved that infinite families of $k_0$-tight optimal double loop networks can be constructed when $A+z-2j\ne0$, $\{N(t)=3t^{2}+(2i-1)t+B$; $B=k_0^2-nk_0+m, t=f^2-if-nk_0+m$, $f=(2i-i^2+4B)p_1^2 p_2^2\cdotsp^2_{k_0^2}e+c$, where $i=1,3, e\ge0, m,n$ are integers\}. The number $N(t)$ of nodes can be a polynomial of degree 4 in $e$ or a polynomial of degree 2 in $e$ with integral coefficients containing a parameter.