有限交换环上Ramanujan单位一-匹配双凯莱图

doi:10.6040/j.issn.1671-9352.0.2022.004

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 59-65.doi: 10.6040/j.issn.1671-9352.0.2022.004

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有限交换环上Ramanujan单位一-匹配双凯莱图

苟小丽,王维忠^*

兰州交通大学数理学院, 甘肃兰州 730070

发布日期:2022-10-06
作者简介:苟小丽(1997— ),女,硕士研究生,研究方向为代数图论. E-mail:xyzkzpy@163.com*通信作者简介:王维忠(1976— ),男,博士,教授,研究方向为代数图论. E-mail:wangwzh@mail.lzjtu.cn
基金资助:
国家自然科学基金资助项目(11961040);甘肃省自然科学基金资助项目(20JR5RA418)

Ramanujan unitary one-matching bi-Cayley graphs over finite commutative rings

GOU Xiao-li, WANG Wei-zhong^*

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

Published:2022-10-06

摘要/Abstract

摘要： 设R是有单位元1≠0的有限交换环,R上的单位一-匹配双凯莱图记为G_R=BC(R; R^×, R^×, {0}),其中R^×表示R单位的集合。若一个k-正则图G的任意具有|λ|≠k的特征值λ满足|λ|≤2(k-1)^1/2,则称这个k-正则图是Ramanujan图。给出R上的单位一-匹配双凯莱图G_R及其线图是Ramanujan图的充要条件。

关键词: 单位一-匹配双凯莱图, 线图, 局部环, 有限交换环, Ramanujan图

Abstract: Let R be a finite commutative ring with unit element 1≠0, and let G_R=BC(R; R^×, R^×, {0})denote the one-matching bi-Cayley graph over R, where R^× is the set of units of R. A k-regular graph G is called a Ramanujan graph if any eigenvalue λ of G with |λ|≠k satisfies |λ|≤2(k-1)1/2. A necessary and sufficient condition for G_R and its line graph to be Ramanujan is given.

Key words: unitary one-matching bi-Cayley graph, line graph, local ring, finite commutative ring, Ramanujan graph

中图分类号:

O157.5

苟小丽,王维忠. 有限交换环上Ramanujan单位一-匹配双凯莱图[J]. 《山东大学学报(理学版)》, 2022, 57(10): 59-65.

GOU Xiao-li, WANG Wei-zhong. Ramanujan unitary one-matching bi-Cayley graphs over finite commutative rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 59-65.

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有限交换环上Ramanujan单位一-匹配双凯莱图

Ramanujan unitary one-matching bi-Cayley graphs over finite commutative rings

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