有限交换环上Ramanujan二次单位一-匹配双凯莱图  

Ramanujan Quadratic Unitary One-matching Bi-CayleyGraphs over Finite Commutative Rings

作　　者：苟小丽 GOU Xiao-li(College of Mothematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《兰州文理学院学报（自然科学版）》2022年第3期17-23,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金项目(11561042,11961040);甘肃省自然科学基金项目(20JR5RA418)。

摘　　要：设R是一个含有单位元1≠0的有限交换环,R×为其单位的集合.令G_(R)=BC(R;T_(R),T_(R),{0})表示R关于T_(R)在加法群上的二次单位一-匹配双凯莱图,其中T_(R)=Q_(R)∪(-Q R),Q_(R)={u^(2):u∈R×}.主要得到了二次单位一-匹配双凯莱图的谱,并刻画了二次单位一-匹配双凯莱图是Ramanujan图的等价条件.LeT_(R)be a finite commutative ring with unit element 1≠0,andR×be its set of units.The quadratic unitary one-matching bi-Cayley graph of R,denoted by G R,is the quadratic one-matching bi-Cayley graphs BC(R;T_(R),T_(R),{0})on the additive group of R with respect to T_(R)=Q_(R)∪(-Q_(R)),where Q_(R)={u^(2):u∈R×}.In this paper,the spectra of such quadratic unitary one-matching bi-Cayley graphs are obtained,and the equivalent conditions of such graphs being Ramanujan are characterized.

关 键 词：二次单位一-匹配双凯莱图 局部环 有限交换环 Ramanujan图 

分 类 号：O157.5[理学—数学]