南方科技大学知识苑(SUSTech KC): Cyclic arcs of Singer type and strongly regular Cayley graphs over finite fields

题名	Cyclic arcs of Singer type and strongly regular Cayley graphs over finite fields
作者	Momihara, Koji 1; Xiang, Qing2,3
通讯作者	Xiang, Qing
发表日期	2022
DOI	10.1016/j.ffa.2021.101953
发表期刊	FINITE FIELDS AND THEIR APPLICATIONS 影响因子和分区
ISSN	1071-5797
EISSN	1090-2465
卷号	77
摘要	In [32], the first author gave a construction of strongly regular Cayley graphs on the additive group of finite fields by using three-valued Gauss periods. In particular, together with the result in [4], it was shown that there exists a strongly regular Cayley graph with negative Latin square type parameters (q(6), r(q(3) +1), -q(3) + r(2)+3r, r(2)+ r), where r = M(q(2) -1) /2, in the following cases: (i) M = 1 and q (math) 3 (mod 4); (ii) M = 3 and q (math) 7 (mod 24); and (iii) M = 7 and q (math) 11,51 (mod 56). The existence of strongly regular Cayley graphs with the above parameters for odd M > 7 was left open. In this paper, we prove that if there is an h, 1 <= h <= M - 1, such that M vertical bar (h(2)+h +1) and the order of 2 in (Z/MZ)(x) is odd, then there exist infinitely many primes q such that strongly regular Cayley graphs with the aforementioned parameters exist. (C) 2021 Elsevier Inc. All rights reserved.
关键词	Cayley graph Chebotarev's density theorem Cyclotomic class Gauss period Strongly regular graph
相关链接	[来源记录]
收录类别	SCI ; EI
语种	英语
学校署名	通讯
资助项目	JSPS[20K03719] ; National Natural Science Foundation of China[12071206] ; Sino-German Mobility Programme[M-0157]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000714427800007
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
EI入藏号	20214511116777
EI主题词	Graph Databases ; Graphic methods
EI分类号	Database Systems:723.3 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4
ESI学科分类	MATHEMATICS
来源库	Web of Science
引用统计	被引频次[WOS]：0
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/255336
专题	理学院_数学系
作者单位	1.Kumamoto Univ, Fac Adv Sci & Technol, Div Nat Sci, 249-1 Kurokami, Kumamoto 8608555, Japan 2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China 3.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen, Shenzhen 518055, Peoples R China
通讯作者单位	数学系; 南方科技大学
推荐引用方式 GB/T 7714	Momihara, Koji,Xiang, Qing. Cyclic arcs of Singer type and strongly regular Cayley graphs over finite fields[J]. FINITE FIELDS AND THEIR APPLICATIONS,2022,77.
APA	Momihara, Koji,&Xiang, Qing.(2022).Cyclic arcs of Singer type and strongly regular Cayley graphs over finite fields.FINITE FIELDS AND THEIR APPLICATIONS,77.
MLA	Momihara, Koji,et al."Cyclic arcs of Singer type and strongly regular Cayley graphs over finite fields".FINITE FIELDS AND THEIR APPLICATIONS 77(2022).