基于有限域上三维非全迷向子空间的辛图  

THE SYMPLECTIC GRAPH CONSTRUCTED BY 3-DIMENSIONAL SYMPLECTIC NON-TOTALLY ISOTROPIC SUBSPACES OVER FINITE FIELDS

作　　者：霍丽君 吴杨 HUO Li-jun;WU Yang(College of Science,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《数学杂志》2024年第4期369-376,共8页Journal of Mathematics

基　　金：重庆市自然科学基金项目(CSTB2022NSCQ-MSX0831,cstc2021jcyj-msxmX0575);重庆理工大学研究生教育高质量发展行动计划资助成果(gzljg2022319);重庆理工大学自科基金培育项目(2022PYZ023);重庆理工大学教育教学改革项目(2023YB115,2024YB08)。

摘　　要：本文以定义在有限域Fq上的2ν维辛空间F_(q)^(2ν)中的三维非全迷向子空间为顶点集构造了一类辛图,记为Γ.Γ的两个顶点V_(1)和V_(2)相邻接当且仅当V_(1)∩V_(2)是F_(q)^(2ν)的一个二维子空间.本文研究了该图的基本性质,计算了图的参数,得到当ν=2时,Γ是一个完全图K_((q+1)(q^(2)+1));当ν=3时,该图是一个8-Deza图;当ν≥4时,该图是一个9-Deza图,由此进一步得到当ν≥3时其直径和围长都是3,并且团数是q^(2v-2)-1/q-1.In this paper,we construct a kind of symplectic graph denoted byΓwith the vertex set consisting of 3-dimensional non-totally isotropic subspaces in the 2ν-dimensional(2ν)symplectic space F_(q)^(2ν)defined over thefinitefield Fq.Two vertices V_(1) and V_(2) ofΓare adjacent(2ν)if and only if V_(1)∩V_(2) is a 2-dimensional subspace of F_(q)^(2ν).We investigate the basic properties of this graph and compute its parameters.We obtain that whenν=2,the graph is a complete graph K(q+1)(q^(2)+1);whenν=3,it is an 8-Deza graph;and whenν≥4,it is a 9-Deza graph.Furthermore,it is shown that the diameter and girth of the graph are both 3 whenν≥3,and the clique number is q^(2ν-2)-1/q-1.

关 键 词：有限域 非全迷向子空间 辛图 d-Deza图 

分 类 号：O157.5[理学—数学]