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

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.