利用Skolem序列构作图K_(m+2)\K_m的图设计

Construct the Graph Designs for the Graphs K_(m+2)\K_m by Using Skolem Sequences

首先应用Skolem序列及Langford序列等直接构作了图G4=K6\K4的 2个无穷类图设计 ,进而将这 2个构作方法推广到更广泛的图类Gm =Km + 2 \Km 上 ,给出了Gm GD(2 (2m +1)t +1)与GmGD(2 (2m +1)t)的直接构造 ,其中m与t为任意正整数 (前者中m奇且t≡ 2 ,3(mod 4 )的情形除外 ) .

Let G m=K m+2\K m.The constructing methods for G m[CD2/5]GD(v) by using Skolem sequen- ces and Langford sequences,are presented.Firstly,the direct constructions of G 4GD(v) for v0,1?(mod?18) are given.Furthermore,the constructing methods are expanded to graph designs G mGD(v) for v0,1?(mod?2(2m+1)),and the relative existence are obtained except the case v=2(2m+1)t+1,where m is odd and t2,3(mod4).