نتایج جستجو برای: regular and strongly regular relations

تعداد نتایج: 16866236  

Journal: :Discrete Mathematics 2002
Frank Fiedler Mikhail H. Klin Mikhail E. Muzychuk

We consider directed strongly regular graphs de2ned in 1988 by Duval. All such graphs with n vertices, n6 20, having a vertex-transitive automorphism group, are determined with the aid of a computer. As a consequence, we prove the existence of directed strongly regular graphs for three feasible parameter sets listed by Duval. For one parameter set a computer-free proof of the nonexistence is pr...

2005
Henk D.L. Hollmann Qing Xiang Jack van Lint

The action of PGL(2,2m) on the set of exterior lines to a nonsingular conic in PG(2,2m) affords an association scheme, which was shown to be pseudocyclic in [H.D.L. Hollmann, Association schemes, Master thesis, Eindhoven University of Technology, 1982]. It was further conjectured in [H.D.L. Hollmann, Association schemes, Master thesis, Eindhoven University of Technology, 1982] that the orbital ...

2006
Hiroyuki NAKASORA H. NAKASORA

Suppose that n is even and a set of n 2 − 1 mutually orthogonal Latin squares of order n exists. Then we can construct a strongly regular graph with parameters (n, n 2 (n−1), n 2 ( 2 −1), n 2 ( 2 −1)), which is called a Latin square graph. In this paper, we give a sufficient condition of the Latin square graph for the existence of a projective plane of order n. For the existence of a Latin squa...

Journal: :Electr. J. Comb. 2008
John B. Polhill

A partial difference set having parameters (n2, r(n − 1), n + r2 − 3r, r2 − r) is called a Latin square type partial difference set, while a partial difference set having parameters (n2, r(n + 1),−n + r2 + 3r, r2 + r) is called a negative Latin square type partial difference set. In this paper, we generalize well-known negative Latin square type partial difference sets derived from the theory o...

Journal: :Journal of Pure and Applied Algebra 1974

2012
Qing Xiang

We survey recent results on constructions of difference sets and strongly regular Cayley graphs by using union of cyclotomic classes of finite fields. Several open problems are raised.

2000
W. Haemers

(otherwise we divide the vector by an appropriate scalar), so w.l.o.g. we have uj = 1 for a certain j ∈ {1, . . . , v}. The absolute value |(A~u)j| of the j-th component of A~u is at most ∑ i∼j |ui|; since the absolute values of all components of ~u are less than or equal to 1, we have ∑ i∼j |ui| ≤ k. On the other hand |(A~u)j| must be equal to |ρuj| = |ρ|, from which we obtain |ρ| ≤ k. If ρ = ...

2017
Qi Kong Ligong Wang QI KONG LIGONG WANG

In this paper, two results about the signless Laplacian spectral radius q(G) of a graph G of order n with maximum degree ∆ are proved. Let Bn = K2 + Kn denote a book, i.e., the graph Bn consists of n triangles sharing an edge. The results are the following: (1) Let 1 < k ≤ l < ∆ < n and G be a connected {Bk+1,K2,l+1}-free graph of order n with maximum degree ∆. Then q(G) ≤ 1 4 [ 3∆ + k − 2l + 1...

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