摘要
令(X,B)为一个v阶的λ-重C_4+e-设计.对于每一个区组B=(u,v,w,x:y)∈B,若删去边{u,x},则得到一个P_5[u,v,w,x,y].令C为删去B中每一个区组的边{u,x}而得到的P_5的集合D,F为被删去的边构成的集合.若F可以被重组成λv(v-1)/40个P_5的集合D,则(X,C∪D)为一个v阶λ-重P_5-设计.称(X,C∪D)为λ-重C_4+e-设计(X,B)的变形.v阶λ-重C_4+e-设计到v阶λ-重P_5-设计的变形存在的充要条件是λv(v-1)≡0(mod40)且v≥5.
Let (X, B) be aλ -fold C4 +e -design of order v. For each block B = (u,v,w,x:y)∈B , if we remove the edge { u,x} , we have a P5 [u, v, w,x,y] . Let d be the collection of P5 s obtained by removing an edge of each block of B, and be the collection of the deleted edges. If can be reassembled into a collection △ of λv(v- 1)/40 P5 s, then (X, c∪△) is a 2 -fold P5 -design of order v. We call (X, c∪△ ) a metamorphosis of the ). -fold C4 + e -design ( X, B) . In this paper, we show that there exists a metamorphosis of a 2 -fold C4 + e -design of order v into λ -fold P5 -design of order vif and only ifλv(v- 1) ≡ 0(mod40) and v ≥ 5 .
出处
《大学数学》
2017年第1期40-45,共6页
College Mathematics
基金
浙江省自然科学基金(LY17A010008)
宁波市自然科学基金(2016A610079)
关键词
图设计
变形
成对平衡设计
graph design
metamorphosis
pairwise balanced design