设Γ是一个直径d≥3的非二部距离正则图,其特征值θ_0>θ_1>…>θ_d.设θ_(1′)∈{θ_1,θ_d),θ_(d′)是θ_(1′)在{θ_1,θ_d}中的余.又设Γ是具有性质E_1 o E_d=|X|^(-1)(q_(1d)^(d-1)E_(d-1)+q_(1d)~dE_d)的E_1 o E_d型距...设Γ是一个直径d≥3的非二部距离正则图,其特征值θ_0>θ_1>…>θ_d.设θ_(1′)∈{θ_1,θ_d),θ_(d′)是θ_(1′)在{θ_1,θ_d}中的余.又设Γ是具有性质E_1 o E_d=|X|^(-1)(q_(1d)^(d-1)E_(d-1)+q_(1d)~dE_d)的E_1 o E_d型距离正则图,σ_0,σ_1,…,σ_d,ρ_0,ρ_1,…,ρ_d和β_0,β_1,…,β_d分别是关于θ_(1′),θ_(d′)和θ_(d-1)的余弦序列.利用上述余弦序列,给出了Γ关于θ_1或θ_d是Q-多项式的充要条件.展开更多
Let F denote the folded （2D ＋ 1）-cube with vertex set X and diameter D ≥ 3. Fix x∈ X. We first define a partial order ≤ on X as follows. For y,z ∈ X let y ≤ z whenever （x,y）＋ （y,z） =- （x, z）. Let R ...Let F denote the folded （2D ＋ 1）-cube with vertex set X and diameter D ≥ 3. Fix x∈ X. We first define a partial order ≤ on X as follows. For y,z ∈ X let y ≤ z whenever （x,y）＋ （y,z） =- （x, z）. Let R （resp. L） denote the raising matrix （resp. lowering matrix） of P. Next we show that there exists a certain linear dependency among RL2, LRL, L2R and L for each given Q-polynomial structure of F. Finally, we determine whether the above linear dependency structure gives this poser a uniform structure or strongly uniform structure.展开更多
文摘设Γ是一个直径d≥3的非二部距离正则图,其特征值θ_0>θ_1>…>θ_d.设θ_(1′)∈{θ_1,θ_d),θ_(d′)是θ_(1′)在{θ_1,θ_d}中的余.又设Γ是具有性质E_1 o E_d=|X|^(-1)(q_(1d)^(d-1)E_(d-1)+q_(1d)~dE_d)的E_1 o E_d型距离正则图,σ_0,σ_1,…,σ_d,ρ_0,ρ_1,…,ρ_d和β_0,β_1,…,β_d分别是关于θ_(1′),θ_(d′)和θ_(d-1)的余弦序列.利用上述余弦序列,给出了Γ关于θ_1或θ_d是Q-多项式的充要条件.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10171006) the Youth Scientific Foundation of Beijing Normal University.
文摘In this paper, it is proved that the girth of a 4-homogeneous bipartite graph with valency greaterthan 2 is at most 12.
基金Supported by the Natural Science Foundation of China(No.11471097)the Innovative Fund Project of Hebei Province(sj.2017084)
文摘Let F denote the folded （2D ＋ 1）-cube with vertex set X and diameter D ≥ 3. Fix x∈ X. We first define a partial order ≤ on X as follows. For y,z ∈ X let y ≤ z whenever （x,y）＋ （y,z） =- （x, z）. Let R （resp. L） denote the raising matrix （resp. lowering matrix） of P. Next we show that there exists a certain linear dependency among RL2, LRL, L2R and L for each given Q-polynomial structure of F. Finally, we determine whether the above linear dependency structure gives this poser a uniform structure or strongly uniform structure.
