Fenggao Li

Metric dimension of some distance-regular graphs

A resolving set of a graph is a set of vertices with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. In this paper, we construct a resolving set of Johnson graphs, doubled Odd graphs, doubled Grassmann graphs and twisted Grassmann graphs, respectively, and obtain the upper bounds on the metric dimension of these graphs.

Association schemes based on attenuated spaces

The subspaces of a given dimension in an attenuated space form the points of an association scheme. If the dimension is maximal, it is the bilinear forms graph, which has been thoroughly studied. In this paper, we discuss the general case, and obtain a family of symmetric association schemes which are a common generalization of the Grassmann schemes and the bilinear forms schemes. Moreover, all the parameters of the association scheme are computed.

Singular linear space and its applications

Abstract As a generalization of attenuated spaces, the concept of singular linear spaces was introduced in [K. Wang, J. Guo, F. Li, Association schemes based on attenuated spaces, European J. Combin. 31 (2010) 297–305]. This paper first gives two anzahl theorems in singular linear spaces, and then discusses their applications to the constructions of Deza digraphs, quasi-strongly regular graphs, lattices and authentication codes.

Metric dimension of symplectic dual polar graphs and symmetric bilinear forms graphs

Abstract In this paper, by constructing resolving sets of symplectic dual polar graphs and symmetric bilinear forms graphs, we obtain upper bounds on their metric dimension.

Incidence matrices of finite attenuated spaces and class dimension of association schemes

Abstract Let d , k , n be integers with 1 ≤ d k ≤ n − d . In Kantor (1972), Kantor proved that the incidence matrix of d -dimensional subspaces versus k -dimensional subspaces of an n -dimensional vector space has full row rank over the real number field R . In this paper, we generalize Kantor’s result to the attenuated space A ( n + l ; F q ) and show that the incidence matrix of d -dimensional subspaces versus k -dimensional subspaces of A ( n + l ; F q ) also has full row rank over R . As an application, we obtain upper bounds for the class dimension of association schemes based on attenuated spaces.

Symplectic graphs modulo pq

Abstract In this paper, we introduce the symplectic graph Sp m ( 2 ν ) modulo m , and show that it is arc transitive. When m is a product of two distinct primes, we determine the suborbits of the symplectic group on Sp m ( 2 ν ) and compute the parameters of Sp m ( 2 ν ) as a quasi-strongly regular graph.

Normalized matching property of subspace posets in finite classical polar spaces

Abstract Let V be one of n-dimensional classical polar spaces over a finite field with q elements. Then all subspaces of V form a graded poset ordered by inclusion, denoted by P n ( q ) . Given a fixed maximal totally isotropic subspace P 0 of V. Then each set P [ t , P 0 ; n ] = { Q ∈ P n ( q ) | dim ( Q ∩ P 0 ) ⩾ t } is a graded subposet of P n ( q ) , where 0 ⩽ t ⩽ ν − 1 . In this paper we show that P [ t , P 0 ; n ] has the NM property, which implies that P [ t , P 0 ; n ] has the strong Sperner property and the LYM property.

On class dimension of flat association schemes in affine and affine-symplectic spaces

In this paper, we obtain upper bounds of the class dimension of flat association schemes in affine and affine-symplectic spaces and construct resolving sets for these schemes.

Normalized Matching Property of Posets Generated by Orbits of Subspaces Under Finite Symplectic Groups

Let be the 2ν-dimensional symplectic space over a finite field 𝔽 q , and let ℳ be a given nontrivial orbit of subspaces in under the symplectic group Sp 2ν(𝔽 q ). Denote by 𝒫 the set of subspaces which are intersections of subspaces in ℳ. By ordering 𝒫 by inclusion, 𝒫 is a finite graded poset. In this article we show that 𝒫 has the normalized matching (NM) property, which implies that 𝒫 has the strong Sperner property and the Lubell-Yamamoto-Meschalkin (LYM) property.

t-Singular Linear Spaces

As a generalization of singular linear spaces, we introduce the concept of t-singular linear spaces, make some anzahl formulas of subspaces, and determine the suborbits of t-singular linear groups.