Strongly regular Cayley graphs from partitions of subdifference sets of the Singer difference sets

被引：8
作者：
Momihara, Koji [1 ]
Xiang, Qing [2 ]
机构：
[1] Kumamoto Univ, Fac Educ, 2-40-1 Kurokami, Kumamoto 8608555, Japan
[2] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2018年 / 50卷
基金：
美国国家科学基金会;
关键词：
Affine polar graph; i-tight set; m-ovoid; Quadratic form; Singer difference set; Strongly regular graph; Subdifference set; GEOMETRY;
D O I：
10.1016/j.ffa.2017.11.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we give a new lifting construction of "hyperbolic" type of strongly regular Cayley graphs. Also we give new constructions of strongly regular Cayley graphs over the additive groups of finite fields based on partitions of subdifference sets of the Singer difference sets. Our results unify some recent constructions of strongly regular Cayley graphs related to m-ovoids and i-tight sets in finite geometry. Furthermore, some of the strongly regular Cayley graphs obtained in this paper are new or nonisomorphic to known strongly regular graphs with the same parameters. (C) 2017 Elsevier Inc. All rights reserved.
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收藏
页码：222 / 250
页数：29
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