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| 摘要: |
| 本文以定义在有限域Fq上的2ν维辛空间Fq(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V1和V2相邻接当且仅当V1∩ V2是Fq(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)(q2+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q2ν-2-1/q-1. |
| 关键词: 有限域 非全迷向子空间 辛图 d-Deza图 |
| DOI： |
| 分类号:O157.5 |
| 基金项目: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). |
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| THE SYMPLECTIC GRAPH CONSTRUCTED BY 3-DIMENSIONAL SYMPLECTIC NON-TOTALLY ISOTROPIC SUBSPACES OVER FINITE FIELDS |
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HUO Li-jun,WU Yang
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| Abstract: |
| In this paper, we construct a kind of symplectic graph denoted by Γ with the vertex set consisting of 3-dimensional non-totally isotropic subspaces in the 2ν-dimensional symplectic space Fq(2ν) defined over the finite field Fq. Two vertices V1 and V2 of Γ are adjacent if and only if V1∩ V2 is a 2-dimensional subspace of Fq(2ν). We investigate the basic properties of this graph and compute its parameters. We obtain that when ν= 2, the graph is a complete graph K(q+1)(q2+1); when ν= 3, it is an 8-Deza graph; and when ν≥ 4, it is a 9-Deza graph. Furthermore, it is shown that the diameter and girth of the graph are both 3 when ν≥ 3, and the clique number is q2ν-2-1/q-1. |
| Key words: flnite fleld non-totally isotropic subspace symplectic graph d-Deza graph |
