On the Nonorientable Genus of the Generalized Unit and Unitary Cayley Graphs of a Commutative Ring

作     者：Mahdi Reza Khorsandi Seyed Reza Musawi 

作者机构：Faculty of Mathematical SciencesShahrood University of Technology P.O.Box 36199-95161ShahroodIran 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2022年第29卷第1期

页      面：167-180页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：unit graph unitary Cayley graph co-maximal graph projective graph nonorientable genus 

摘      要：Let R be a commutative ring and U(R)the multiplicative group of unit elements of *** 2012,Khashyarmanesh et *** the generalized unit and unitary Cayley graph,T(R,G,S),corresponding to a multiplicative subgroup G of U(R)and a nonempty subset S of G with S^(-1)={s^(-1)|s∈S}■S,asthegraphwithvertexsetR and two distinct vertices x and y being adjacent if and only if there exists s∈S such that x+sy∈*** this paper,we characterize all Artinian rings R for which T(R,U(R),S)is *** leads us to determine all Artinian rings whose unit graphs,unitary Cayley graphs and co-maximal graphs are *** addition,we prove that for an Artinian ring R for which T(R,U(R),S)has finite nonorientable genus,R must be a finite ***,it is proved that for a given positive integer k,the number of finite rings R for which T(R,U(R),S)has nonorientable genus k is finite.