共查询到20条相似文献,搜索用时 15 毫秒
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Blocks of the unique Steiner system S(5, 8, 24) are called octads. The group PSL(2, 23) acts as an automorphism group of this Steiner system, permuting octads transitively. Inspired by the discovery of a 5-(24, 10, 36) design by Gulliver and Harada, we enumerate all 4- and 5-designs whose set of blocks are union of PSL(2, 23)-orbits on 10-subsets containing an octad. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 147–155, 1999 相似文献
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Dean Crnković B.G. Rodrigues Sanja Rukavina Vladimir D. Tonchev 《Discrete Mathematics》2017,340(10):2472-2478
This paper completes the enumeration of quasi-symmetric 2- designs supported by the dual code of the binary linear code spanned by the lines of , initiated in Rodrigues and Tonchev (2015). It is shown that supports exactly 30,264 nonisomorphic quasi-symmetric 2- designs. The automorphism groups of the related strongly regular graphs are computed. 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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Leonard H. Soicher 《Journal of Combinatorial Theory, Series A》2010,117(7):799-1141
The concept of intersection numbers of order r for t-designs is generalized to graphs and to block designs which are not necessarily t-designs. These intersection numbers satisfy certain integer linear equations involving binomial coefficients, and information on the non-negative integer solutions to these equations can be obtained using the block intersection polynomials introduced by P.J. Cameron and the present author. The theory of block intersection polynomials is extended, and new applications of these polynomials to the studies of graphs and block designs are obtained. In particular, we obtain a new method of bounding the size of a clique in an edge-regular graph with given parameters, which can improve on the Hoffman bound when applicable, and a new method for studying the possibility of a graph with given vertex-degree sequence being an induced subgraph of a strongly regular graph with given parameters. 相似文献
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YANG BENFU 《高校应用数学学报(英文版)》1994,9(3):291-297
USINGFINITEGEOMETRIESTOCONSTRUCT3-PBIB(2)DESIGNSAND3-DESIGNS¥YANGBENFU(DepartmentofMathematics,ChengduTeachersCollege,Chengdu... 相似文献
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本文结出图K_n和K_(n,n)的7-匹配设计的存在性和由两个简单的(n,k,λ)-设计(i=1,2)构造简单的(n,k,λ+λ_2)设计的条件. 相似文献
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A Deza graph with parameters is a ‐regular graph on vertices in which the number of common neighbors of two distinct vertices takes one of the following values: or , where . In the previous papers Deza graphs with were characterized. In this paper, we characterize Deza graphs with . 相似文献
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We study the perfect 2‐colorings (also known as the equitable partitions into two parts or the completely regular codes with covering radius 1) of the Johnson graphs . In particular, we classify all the realizable quotient matrices of perfect 2‐colorings for odd v. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 21: 232–252, 2013 相似文献
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Etsuko Bannai 《Journal of Algebraic Combinatorics》2006,24(4):391-414
Neumaier and Seidel (1988) generalized the concept of spherical designs and defined Euclidean designs in ℝ
n
. For an integer t, a finite subset X of ℝ
n
given together with a weight function w is a Euclidean t-design if holds for any polynomial f(x) of deg(f)≤ t, where {S
i
, 1≤ i ≤ p} is the set of all the concentric spheres centered at the origin that intersect with X, X
i
= X∩ S
i
, and w:X→ ℝ> 0. (The case of X⊂ S
n−1 with w≡ 1 on X corresponds to a spherical t-design.) In this paper we study antipodal Euclidean (2e+1)-designs. We give some new examples of antipodal Euclidean tight 5-designs. We also give the classification of all antipodal Euclidean tight 3-designs, the classification of antipodal Euclidean tight 5-designs supported by 2 concentric spheres. 相似文献
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《Discrete Mathematics》2021,344(12):112623
In this paper, we construct two new symmetric designs with parameters 2- as designs invariant under certain subgroups of the full automorphism group of the Higman design. One is self-dual and has the full automorphism group of order 11520 and the other one is not self-dual and has the full automorphism group of order 2520. 相似文献
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OD-characterization of Almost Simple Groups Related to U3(5) 总被引:1,自引:0,他引:1
Let G be a finite group with order |G|=p1^α1p2^α2……pk^αk, where p1 〈 p2 〈……〈 Pk are prime numbers. One of the well-known simple graphs associated with G is the prime graph (or Gruenberg- Kegel graph) denoted .by г(G) (or GK(G)). This graph is constructed as follows: The vertex set of it is π(G) = {p1,p2,…,pk} and two vertices pi, pj with i≠j are adjacent by an edge (and we write pi - pj) if and only if G contains an element of order pipj. The degree deg(pi) of a vertex pj ∈π(G) is the number of edges incident on pi. We define D(G) := (deg(p1), deg(p2),..., deg(pk)), which is called the degree pattern of G. A group G is called k-fold OD-characterizable if there exist exactly k non- isomorphic groups H such that |H| = |G| and D(H) = D(G). Moreover, a 1-fold OD-characterizable group is simply called OD-characterizable. Let L := U3(5) be the projective special unitary group. In this paper, we classify groups with the same order and degree pattern as an almost simple group related to L. In fact, we obtain that L and L.2 are OD-characterizable; L.3 is 3-fold OD-characterizable; L.S3 is 6-fold OD-characterizable. 相似文献