نتایج جستجو برای: strongly regular graph

تعداد نتایج: 520829  

2013
Gennian Ge Qing Xiang Tao Yuan

We give a construction of strongly regular Cayley graphs on finite fields Fq by using union of cyclotomic classes and index 4 Gauss sums. In particular, we obtain two infinite families of strongly regular graphs with new parameters.

2003
KA HIN LEUNG

It is known that a strongly regular semi-Cayley graph (with respect to a group G) corresponds to a triple of subsets (C, D, D') of G. Such a triple (C, D, D') is called a partial difference triple. First, we study the case when D U D' is contained in a proper normal subgroup of G. We basically determine all possible partial difference triples in this case. In fact, when \G\ f 8 nor 25, all part...

Journal: :Graphs and Combinatorics 2012
Bart De Bruyn

Intriguing sets of vertices have been studied for several classes of strongly regular graphs. In the present paper, we study intriguing sets for the graphs Γn, n ≥ 2, which are defined as follows. Suppose Q(2n, 2), n ≥ 2, is a nonsingular parabolic quadric of PG(2n, 2) and Q+(2n − 1, 2) is a nonsingular hyperbolic quadric obtained by intersecting Q(2n, 2) with a suitable nontangent hyperplane. ...

2005
RUDI SALOMON

We present a Prym construction which associates abelian varieties to vertex-transitive strongly regular graphs. As an application we construct Prym-Tyurin varieties of arbitrary exponent ≥ 3, generalizing a result by Lange, Recillas and Rochas.

Journal: :Australasian J. Combinatorics 1993
Watcharaphong Ananchuen Lou Caccetta

ON GRAPHS SATISFYING A STRONG ADJACENCY PROPERTY Y. Ananchuen and L. Caccetta School of Mathematics and Statistics Curtin University of Technology GPO Box U1987 Perth 6001 Western Australia. Dedicated to the memory of Alan Rahilly, 1947 1992 Let m and n be nonnegative integers and k be a positive integer. A graph G is said to have property P*(m,n,k) if for any set of m + n distinct vertices of ...

2003
RANDALL J. ELZINGA

Dedicated to the memory of Prof. Dom de Caen Abstract. Given λ and μ, it is shown that, unless one of the relations (λ− μ)2 = 4μ, λ− μ = −2, (λ− μ)2 + 2(λ− μ) = 4μ is satisfied, there are only finitely many parameter sets (v, k, λ, μ) for which a strongly regular graph with these parameters could exist. This result is used to prove as special cases a number of results which have appeared in pre...

Journal: :Australasian J. Combinatorics 2001
Brendan D. McKay Edward Spence

In a previous paper an incomplete investigation into regular two-graphs on 36 vertices established the existence of at least 227. Using a more efficient algorithm, the two authors have independently verified that in fact these 227 comprise the complete set. An immediate consequence of this is that all strongly regular graphs with parameters (35,16,6,8), (36,14,4,6), (36,20,10,12) and their comp...

1998
A. E. BROUWER QING XIANG

We consider strongly regular graphs defined on a finite field by taking the union of some cyclotomic classes as difference set. Several new examples are found.

2014
Vasco Moço Mano

Considering the Euclidean Jordan algebra of the real symmetric matrices endowed with the Jordan product and the inner product given by the usual trace of matrices, we construct an alternating Schur series with an element of the Jordan frame associated to the adjacency matrix of a strongly regular graph. From this series we establish necessary conditions for the existence of strongly regular gra...

2010
Ada Chan

Forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph X contains a Hadamard matrix then X is of Latin square type or of negative Latin square type [8]. We extend their result to complex Hadamard matrices and find only three additional families of parameters for which the strongly regular graphs have complex Hadamard matrices in their adjacency alg...

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