Results 21 to 30 of about 29,931 (112)
Hemisystems and strongly regular graphs
Discrete Applied MathematicsIn a recent paper, it was constructed a family of hemisystems of H(3,p2), for every prime p of the form p=1+4a2, stabilised by PSL(2,p)×C[Formula presented]. In the case p=5, the full automorphism group is 3.A7, and the hemisystem is isomorphic to a sporadic one described by A. Cossidente and T. Penttila in 2005.
Pallozzi Lavorante V. +2 more
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On Strongly Regular Graphs withμ= 1
European Journal of Combinatorics, 2001 The paper looks at strongly regular graphs in which each pair of non-adjacent vertices has exactly one common neighbour. Relationships between the parameters of such graphs are explored as are some of the associated particle linear spaces and distance-regular graphs.
J. Deutsch, P. H. Fisher
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Strongly Regular Fusions of Tensor Products of Strongly Regular Graphs
Rocky Mountain Journal of Mathematics, 1994 Let \(G\) and \(H\) be strongly regular graphs with (0, 1)-adjacency matrices \(A_ 0= I\), \(A_ 1\), \(A_ 2= J-I- A_ 1\) and \(B_ 0= I\), \(B_ 1,\) \(B_ 2= J- I- B_ 1\) respectively. The tensor product \(G\otimes H\) is defined to be the nine class association scheme with adjacency matrices \(A_ i\otimes B_ j\). By combining (fusing) some of these nine
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Distance regular graphs of diameter 3 and strongly regular graphs
Discrete Mathematics, 1984 In a paper by \textit{N. L. Biggs} [Ann. Discrete Math. 15, 69-80 (1982; Zbl 0506.05057)], two parameter sets for distance regular graphs that are antipodal covers of a complete graph were mentioned for which the existence of a corresponding graph was unknown.
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q-analogs of strongly regular graphs
Linear Algebra and its ApplicationsWe introduce the notion of q-analogs of strongly regular graphs and give several examples of such structures. We prove a necessary condition on the parameters, show the connection to designs over finite fields, and present a classification.
Michael Braun +4 more
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Distance-Regular Graphs with Strongly Regular Subconstituents [PDF]
Journal of Algebraic Combinatorics, 1997 The main result of the article is a theorem about distance-regular graphs of diameter \(d\geq 3\) with all subconstituents being strongly regular graphs. The author shows that these are precisely the Taylor graphs \((d=3\) and \(|\Gamma_3 (u) |=1)\) or graphs with \(a_1= 0\), \(a_i\leq 1\) for \(2\leq i\leq d\).
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Bent Functions and Strongly Regular Graphs
QeiosThe family of bent functions is a known class of Boolean functions, which have a great importance in cryptography. The Cayley graph defined on \(\mathbb{Z}_{2}^{n}\) by the support of a bent function is a strongly regular graph \(srg(v,k,\lambda,\mu)\), with \(\lambda=\mu\). In this note we list the parameters of such Cayley graphs.
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On regular and strongly-regular self-complementary graphs
Discrete Mathematics, 1985 A graph G is called self-complementary, if it is isomorphic to its own complement. The symbol \({\mathcal C}(G)\) denotes the set of permutations of the vertex set V(G) of G which induce isomorphisms of G onto its complement. Further F(G) is the set of all vertices u of G for which there exists \(\sigma\in {\mathcal C}(G)\) such that \(\sigma (u)=u ...
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A directed graph version of strongly regular graphs
Journal of Combinatorial Theory, Series A, 1988 The paper gives existence and nonexistence conditions of a directed graph version of strongly regular graphs whose adjacency matrices satisfy the equations \[ A^ 2+(u-v)A-(t-u)I=uJ\quad \] \[ AJ=JA=kJ \] where A is the adjacency matrix, I the identity matrix, J the matrix of all l's and u, v, t, k are the parameters.
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Groups acting on trees with Tits' independence property (P): With an appendix by Stephan Tornier. [PDF]
Math AnnReid CD, Smith SM.
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