奇特征有限域上的辛图  

Symplectic graphs over finite fields of odd characteristic

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作  者:苏磊磊 南基洙[1] 韦扬江 SU Leilei;NAN Jizhu;WEI Yangjiang(School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;School of Mathematics and Statistics, Nanning Normal University, Nanning 530001, China)

机构地区:[1]大连理工大学数学科学学院,辽宁大连116024 [2]南宁师范大学数学与统计学院,广西南宁530001

出  处:《大连理工大学学报》2022年第1期102-110,共9页Journal of Dalian University of Technology

基  金:国家自然科学基金资助项目(11771176).

摘  要:令F_(q)是特征数为奇数的有限域.选取辛空间F^((2ν))_(q)中所有二维全迷向子空间作为顶点来构造辛图,并规定两个顶点是相邻的当且仅当它们的交是一维子空间.通过计算可知,当ν=3时,辛图是4-Deza图;当ν≥4时,辛图是5-Deza图.此外,研究了辛图次成分的正则性,并且计算了次成分中两个不同顶点之间的参数.结果表明,当ν=2时,辛图的两个次成分都是正则的;而当ν≥3时,辛图的两个次成分都不是正则的.Let F_(q) be a finite field of odd characteristic,a symplectic graph whose vertex set is all two dimensional totally isotropic subspaces of the symplectic space F^((2ν))_(q) is constructed,and two vertices are adjacent if and only if their intersection is a one dimensional subspace.By calculating,symplectic graph is a 4-Deza graph whenν=3 and a 5-Deza graph whenν≥4.Moreover,the regularity of the subconstituents of the symplectic graph is studied and the parameter of two distinct vertices of the subconstituents is calculated.The results show that two subconstituents are regular whenν=2 and not regular whenν≥3.

关 键 词:辛图 d-Deza图 次成分 距离 

分 类 号:O157.5[理学—数学]

 

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