Let Fq be a finite field of odd characteristic, m, v the integers with 1 ≤ m ≤ v and K a 2v × 2v nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2v（q, m） relative to K...Let Fq be a finite field of odd characteristic, m, v the integers with 1 ≤ m ≤ v and K a 2v × 2v nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2v（q, m） relative to K over Fq is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2v-dimensional symplectic space Fq（2v） as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQw is 1 and the dimension of P ∩ Q is m - 1. It is proved that the full automorphism group of the graph GSp2v（q, m） is the projective semilinear symplectic group P∑p（2v, q）.展开更多
In this paper, we construct some 1 1/2-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1^-des...In this paper, we construct some 1 1/2-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1^-designs yield six infinite families of directed strongly regular graphs.展开更多
In this paper, we construct some 1（1/2）-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the unitary space. Phrthermore, these 1（1/2）-designs yield six infinite fami...In this paper, we construct some 1（1/2）-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the unitary space. Phrthermore, these 1（1/2）-designs yield six infinite families of directed strongly regular graphs.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.10990011,11271004 and 61071221)the Doctoral Program of Higher Education of China(Grant No.20100001110007)the Natural Science Foundation of Hebei Province(Grant No.A2009000253)
文摘Let Fq be a finite field of odd characteristic, m, v the integers with 1 ≤ m ≤ v and K a 2v × 2v nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2v（q, m） relative to K over Fq is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2v-dimensional symplectic space Fq（2v） as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQw is 1 and the dimension of P ∩ Q is m - 1. It is proved that the full automorphism group of the graph GSp2v（q, m） is the projective semilinear symplectic group P∑p（2v, q）.
基金Supported by National Natural Science Foundation of China(Grant No.61370187)
文摘In this paper, we construct some 1 1/2-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1^-designs yield six infinite families of directed strongly regular graphs.
文摘In this paper, we construct some 1（1/2）-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the unitary space. Phrthermore, these 1（1/2）-designs yield six infinite families of directed strongly regular graphs.
