作者机构：
[Huang, Li-Ping] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Peoples R China.;[Lv, Benjian; Wang, Kaishun] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China.;[Lv, Benjian; Wang, Kaishun] Beijing Normal Univ, Lab Math Com Sys, Beijing 100875, Peoples R China.
通讯机构：
[Huang, Li-Ping] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Peoples R China.
关键词：
Automorphism;Grassmann graph;Grassmann space;Maximum clique;Residue class ring
摘要：
Let Z(ps) be the residue class ring of integers modulo p(s), where p is a prime number and s is a positive integer. The Grassmann graph over Z(ps), denoted by G(n, m, p(s)), has the vertex set all m-subspaces of Z(ps)(n) (n > m >= 1), and two vertices are adjacent if and only if their intersection is of dimension m - 1. We characterize the automorphisms of G(n, m, p(s)) as follows. Let n >= 2m >= 4 and let phi is an element of Aut(G(n, m, p(s))). Then either phi(X) = XU for all X is an element of V(G(n, m, p(s))), or n = 2m and phi(X)= (XU)(perpendicular to) for all X is an element of V(G(2m, m, p(s)), where U is a fixed invertible matrix and (XU)(perpendicular to) is the dual subspace of XU. This result also extends Chow's theorem for the geometry of Grassmann space. (C) 2019 Elsevier B.V. All rights reserved.
期刊：
Finite Fields and Their Applications,2019年55:284-304 ISSN：1071-5797
通讯作者：
Huang, Li-Ping
作者机构：
[Huang, Li-Ping] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Hunan, Peoples R China.
通讯机构：
[Huang, Li-Ping] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Hunan, Peoples R China.
关键词：
Quadratic forms graph;Endomorphism;Pseudo-core;Core;Maximal clique
摘要：
A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or a colouring. A graph G is a core if every endomorphism of G is an automorphism. Let F-q be the finite field with q elements where q is a power of an odd prime number. The quadratic forms graph, denoted by Quad(n, q) where n >= 2, has all quadratic forms on F-q(n) as vertices and two vertices f and g are adjacent whenever rk(f - g) = 1 or 2. We prove that every Quad(n, q) is a pseudo-core. Further, when n is even, Quad(n, q) is a core. When n is odd, Quad(n, q) is not a core. On the other hand, we completely determine the independence number of Quad(n, q). (C) 2018 Elsevier Inc. All rights reserved.
摘要：
A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or a colouring. An interesting problem in graph theory is to distinguish whether a graph is a core. The twisted Grassmann graphs, constructed by van Dam and Koolen in (Invent Math 162:189-193, 2005), are the first known family of non-vertex-transitive distance-regular graphs with unbounded diameter. In this paper, we show that every twisted Grassmann graph is a pseudo-core.
期刊：
Graphs and Combinatorics,2017年33(6):1607-1620 ISSN：0911-0119
通讯作者：
Huang, Li-Ping
作者机构：
[Huang, Li-Ping] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Hunan, Peoples R China.;[Lv, Benjian] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China.;[Lv, Benjian] Beijing Normal Univ, Lab Math Com Syst, Beijing 100875, Peoples R China.
通讯机构：
[Huang, Li-Ping] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Hunan, Peoples R China.
摘要：
A graph G is a core if every endomorphism of G is an automorphism. Let J(q) (n, m) be the Grassmann graph with parameters q, m, n. We prove that many Grassmann graphs are cores, and both J(2)(2k, 2) and J(q) (2k, 2) are not cores. We also obtain the independence number of Jq (n, 2). In further to study cores and coding theory, it is important to estimate the upper bound of the independence number of J(q) (n, m). Using a vertex-transitive subgraph of J(q) (n, m), we obtain upper bounds on the independence number of J(q) (n, m), which are also an improvement of bounds for the size of constant dimension codes in a 2011 paper of Etzion and Vardy.
摘要：
A graph G is a core if every endomorphism of G is an automorphism. A graph is called a pseudo-core if every its endomorphism is either an automorphism or a colouring. Suppose that J(q) (n, m) is a Grassmann graph over a finite field with q elements. We show that every Grassmann graph is a pseudo-core. Moreover, J(2) (4, 2) is not a core and J(q) (2k + 1, 2) (k >= 2) is a core.
关键词：
Alternating forms graph;Endomorphism;Core;Pseudo-core;Maximum clique
摘要：
A graph G is a pseudo-core if every endomorphism of G is either an automorphism or a colouring. Let F q be the finite field with q elements and let Alt ( m , q ) ( m 4 ) be the alternating forms graph on the vector space F q m . We prove that Alt ( m , q ) is a pseudo-core. Moreover, if m is odd, then Alt ( m , q ) is a core. If both m and q are even, then Alt ( m , q ) is not a core. A graph G is a pseudo-core if every endomorphism of G is either an automorphism or a colouring. Let F q be the finite field with q elements and let Alt ( m , q ) ( m 4 ) be the alternating forms graph on the vector space F q m . We prove that Alt ( m , q ) is a pseudo-core. Moreover, if m is odd, then Alt ( m , q ) is a core. If both m and q are even, then Alt ( m , q ) is not a core.
期刊：
Linear Algebra and its Applications,2014年447:2-25 ISSN：0024-3795
通讯作者：
Sze, Nung-Sing
作者机构：
[Huang, Li-Ping] Changsha Univ Sci & Technol, Sch Math & Comp Sci, Changsha 410004, Hunan, Peoples R China.;[Huang, Zejun; Sze, Nung-Sing] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China.;[Li, Chi-Kwong] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA.;[Li, Chi-Kwong] Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China.
通讯机构：
[Sze, Nung-Sing] H;Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China.
关键词：
Matrix algebra;Networks (circuits);Chromatic number;Endomorphism;Finite fields;Graph;Independence number;Graph theory
会议名称：
7th International Conference of Matrices and Operators (MAO 2012)
会议时间：
JUL 13-16, 2012
会议地点：
Harbin Engn Univ, Harbin, PEOPLES R CHINA
会议主办单位：
Harbin Engn Univ
关键词：
ring;full matrix ring;homomorphism;set of matrix units;general linear group
摘要：
Let R, R' be rings with an identity element. We discuss the ring homomorphisms from M-n (R) to R', and the sets of matrix units in a ring. Also, we give a correctional proof of an important proposition on the group homomorphisms between linear groups over rings.
作者机构：
[Li-Ping Huang; Dan-Dan Wang; Fei-Jie Peng] School of Mathematics and Computing Science,Changsha University of Science and Technology
会议名称：
The Sixth International Conference of Matrices and Operators(第六届矩阵与算子国际学术研讨会)
会议时间：
2011-07-08
会议地点：
成都
会议论文集名称：
The Sixth International Conference of Matrices and Operators(第六届矩阵与算子国际学术研讨会)论文集
关键词：
matrix;Bezout domain;weak semi-isomorphism;Jordan ring
摘要：
Let R,R' be Bezout domains. This paper proves that: If φ : Rn×n→Rn×n is a weak semi-isomorphism, then φ=±f, where f is either a ring isomorphism or a ring anti-isomorphism.
作者机构：
[Li-Ping Huang; Ling-Ling Wang; Dan-Dan Wang] School of Mathematics and Computing Science,Changsha University of Science and Technology
会议名称：
The Sixth International Conference of Matrices and Operators(第六届矩阵与算子国际学术研讨会)
会议时间：
2011-07-08
会议地点：
成都
会议论文集名称：
The Sixth International Conference of Matrices and Operators(第六届矩阵与算子国际学术研讨会)论文集
关键词：
matrix equation
摘要：
Let F be a field, R be a finite dimensional central simple F-algebra with an involution. This paper discusses the solvability of the matrix equation ∑AlXBl=C with X=X.
通讯机构：
[Huang, Li-Ping] C;Changsha Univ Sci & Technol, Sch Math & Comp Sci, Changsha 410076, Hunan, Peoples R China.
关键词：
Adjacency relations;Characteristic 2;Distance geometry;Distance graphs;Division ring with an involution;Geometry of matrices;Graph isomorphism;Hermitian matrices;Positive integers;Surjective;Vertex set;Computational geometry;Set theory;Theorem proving
摘要：
<jats:title>Abstract</jats:title>
<jats:p>Let <jats:italic>R</jats:italic> be any commutative principal ideal domain (PID), and let <jats:italic>n</jats:italic> be an integer ≥ 2. Denote by 𝕀<jats:sub>
<jats:italic>n</jats:italic> − 1</jats:sub> the set of all (<jats:italic>n</jats:italic> − 1)-dimensional self-dual flats of a polarity in the projective geometry ℙ(<jats:italic>R</jats:italic>
<jats:sup>2<jats:italic>n</jats:italic>
</jats:sup>). The geometric character of 𝕀<jats:sub>
<jats:italic>n</jats:italic> − 1</jats:sub> is discussed. Two self-dual flats <jats:italic>A, B</jats:italic> ∈ 𝕀<jats:sub>
<jats:italic>n</jats:italic> − 1</jats:sub> are said to be adjacent if dim(<jats:italic>A</jats:italic> ∩ <jats:italic>B</jats:italic>) = <jats:italic>n</jats:italic> − 2. We prove that <jats:italic>ϕ</jats:italic> : 𝕀<jats:sub>
<jats:italic>n</jats:italic> − 1</jats:sub> → 𝕀<jats:sub>
<jats:italic>n</jats:italic> − 1</jats:sub> is an adjacency preserving surjection if and only if <jats:italic>ϕ</jats:italic> is an adjacency preserving bijection in both directions. Chow's theorem on the self-dual flats is extended as follows: If the polarity is the symplectic polarity and <jats:italic>ϕ</jats:italic> : 𝕀<jats:sub>
<jats:italic>n</jats:italic> − 1</jats:sub> → 𝕀<jats:sub>
<jats:italic>n</jats:italic> − 1</jats:sub> is an adjacency preserving surjection, then <jats:italic>ϕ</jats:italic> is induced by a collineation on ℙ(<jats:italic>R</jats:italic>
<jats:sup>2<jats:italic>n</jats:italic>
</jats:sup>).</jats:p>
