共查询到18条相似文献,搜索用时 93 毫秒
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设г是直径为d且型为(a 1,3)的距离正则图,其中a≥2.用l(c,a,b)表示交叉阵列ι(г)中列(c,a,6)t的个数,记r=r(г)=l(c1,a1,b1),8=8(г)=l(Cr 1,ar 1,br 1)及t=t(г)=l(cr s 1,ar s 1,br s 1).那末,若Cr 1=3,ar 1=4a或3a 1,则d=r t 2. 相似文献
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设Γ是直径为d且型为(α 1,3)的距离正则图,其中α≥2.用l(c,a,b)表示交叉阵列l(Γ)中列(c,a,b)~t的个数,记r=r(Γ)=l(c_1,a_1,b_1),s=s(Γ)=l(c_(r 1),a(r 1),b_(r 1)).那末,若c_(r 1)=3且a_(r 1)=3a,则d=r s 1,c_d=4且Γ为正则拟2d边形. 相似文献
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链状正则图的平均距离 总被引:1,自引:0,他引:1
本文构造了一类链状正则图G_k∶δ,求出了它们的平均距离D(G_k.δ),并得到关系式上式等号成立当且仅当δ=4f且k=0.这个估计式指出了施容华猜想[1]D(G)≤n/(δ 1)不成立. 文中进一步证明了这一类链状正则图有最大的直径,所以可以作出猜想: 若G是n阶连通图,则D(G)<(n 1)/(δ 1),其中δ是图G的最小度。 相似文献
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利用距离正则图的特征值方法,得到如下结论:设Γ是一个有序对为(3,3)正则拟多边形,如果d=r+1,则cd≠1,2,3. 相似文献
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设Г是一个直径d ≥ 3的非二部距离正则图,其特征值θ0>θ1>…>θ<,d.设θ1 ∈{θ1,θd),θd,是θ1在{θ1,θd}中的余.又设Г是具有性质E1οEd=|X|-1>(qd-11dEd-1 qd1dEd)的E1○Ed型距离正则图,σ0,σ1,…,σd,ρ0,ρ1,…,ρd和β0,β1,…,βd分别是关于θ1',θd和θd-1'的余弦序列.利用上述余弦序列,给出了Г关于θ1或θd是 Q-多项式的充要条件. 相似文献
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给出了具有广义可行性余弦序列的E1?Ed型距离正则图的特征,并计算了这类图的交叉数. 相似文献
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Paul Terwilliger 《Journal of Combinatorial Theory, Series B》1985,39(3):265-281
We study the structure of a distance-regular graph Γ with girth 3 or 4. First, we find some relationships among the intersection numbers of Γ when Γ contains a cycle {u1, u2, u3, u4} with ?(u1, u3) = ?(u2, u4) = 2. These relationships imply the diameter d, valency k, and intersection numbers a1 and cd of Γ are related by . Next, we show subgraphs induced by vertex neighbourhoods in distance-regular graphs where cycles mentioned above do not exist are related to certain strongly regular graphs. 相似文献
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Laihao Ding Guan-Huei Duh Guanghui Wang Tsai-Lien Wong Jianliang Wu Xiaowei Yu Xuding Zhu 《Discrete Mathematics》2019,342(1):279-284
A graph is -choosable if the following holds: For any list assignment which assigns to each vertex a set of real numbers, and assigns to each edge a set of real numbers, there is a total weighting such that for , and for every edge . This paper proves that if is a connected graph of maximum degree , then is -choosable. 相似文献
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Let n be a positive integer. In this paper, using the results on the existence of primitive divisors of Lucas numbers and some properties of quadratic and exponential diophantine equations, we prove that if n ≡ 3 (mod 6), then the equation x 2 + (3n 2 + 1) y = (4n 2 + 1) z has only the positive integer solutions (x, y, z) = (n, 1, 1) and (8n 3 + 3n, 1, 3). 相似文献
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J. H. Koolen 《European Journal of Combinatorics》2002,23(8):987
Bannai and Ito conjectured in a 1987 paper that there are finitely many distance-regular graphs with fixed degree that is greater than two. In a series of papers they showed that their conjecture held for distance-regular graphs with degrees 3 or 4. In this paper we prove that the Bannai–Ito conjecture holds for degrees 5–7. 相似文献
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We study the relation between distance-regular graphs and (α, β)-geometries in two different ways. We give necessary and sufficient
conditions for the neighbourhood geometry of a distance-regular graph to be an (α, β)-geometry, and describe some (classes
of) examples. On the other hand, properties of certain regular two-graphs allow us to construct (0, α)-geometries on the corresponding
Taylor graphs. 相似文献
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《数学的实践与认识》2015,(23)
针对超椭圆曲线y~k=x(x+1)(x+3)(x+4)上是否存在有理点这一问题,运用了分类讨论的方法求解出当k≥3且k≠4时,该超椭圆曲线上的有理点只有(0,0);(-1,0);(-3,0);(-4,0). 相似文献