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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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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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In this note we classify the regular near polygons of order (s, 2). 相似文献
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D.G. Fon-Der-Flaass 《Journal of Algebraic Combinatorics》1993,2(1):49-56
We prove that a distance-regular graph with intersection array (5, 4, 3, 3; 1, 1, 1, 2) does not exist. The proof is purely combinatorial and computer-free. 相似文献
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In this note we will generalize the Higman-Haemers inequalities for generalized polygons to thick regular near polygons. 相似文献
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Frank de Clerck Stefaan de Winter Elisabeth Kuijken Cristina Tonesi 《Designs, Codes and Cryptography》2006,38(2):179-194
We introduce distance-regular (0,α)-reguli and show that they give rise to (0,α)-geometries with a distance-regular point graph. This generalises the SPG-reguli of Thas [14] and the strongly regular (α,β)-reguli of Hamilton and Mathon [9], which yield semipartial geometries and strongly regular (α,β)-geometries, respectively. We describe two infinite classes of examples, one of which is a generalisation of the well-known
semipartial geometry Tn*(B) arising from a Baer subspace PG(n, q) in PG(n, q2).
Research Fellow supported by the Flemish Institute for the Promotion of Scientific and Technological Research in Industry
(IWT), grant no. IWT/SB/13367/Tonesi
Research assistant of the Fund for Scientific Research Flanders (FWO-Vlaanderen). 相似文献
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Valuations of dense near polygons were introduced in 16 . In the present paper, we classify all valuations of the near hexagons ??1 and ??2, which are related to the respective Witt designs S(5,6,12) and S(5,8,24). Using these classifications, we prove that if a dense near polygon S contains a hex H isomorphic to ??1 or ??2, then H is classical in S. We will use this result to determine all dense near octagons that contain a hex isomorphic to ??1 or ??2. As a by‐product, we obtain a purely geometrical proof for the nonexistence of regular near 2d‐gons, d ≥ 4, whose parameters s, t, ti (0 ≤ i ≤ d) satisfy (s, t2, t3) = (2, 1, 11) or (2, 2, 14). The nonexistence of these regular near polygons can also be shown with the aid of eigenvalue techniques. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 214–228, 2006 相似文献
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Michael Krivelevich Benny Sudakov Nicholas Wormald 《Random Structures and Algorithms》2011,38(3):235-250
An old problem of Erd?s, Fajtlowicz, and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on vertices. Motivated by this problem, we consider the order of such a subgraph in a typical graph on vertices, i.e., in a binomial random graph . We prove that with high probability a largest induced regular subgraph of has about vertices. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 38, 235–250, 2011 相似文献