Finite commutative rings whose line graphs of comaximal graphs have genus at most two

被引:0
|
作者
Su, Huadong [1 ]
Huang, Chunhong [2 ]
机构
[1] Beibu Gulf Univ, Coll Sci, Eastern Michigan Joint Coll Engn, Qinzhou 535011, Peoples R China
[2] Guangxi Sci & Technol Normal Univ, Sch Math & Comp Sci, Laibin 545004, Peoples R China
来源
关键词
finite commutative ring; comaximal graph; line graph; genus; induced subgraph; IDEAL GRAPH;
D O I
10.15672/hujms.1256413
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let R be a ring with identity. The comaximal graph of R , denoted by F(R), R ) , is a simple graph with vertex set R and two different vertices a and b are adjacent if and only if aR + bR = R . Let F2(R) 2 ( R ) be a subgraph of F(R) R ) induced by R \{ U ( R ) U J ( R ) }. In this paper, we investigate the genus of the line graph L (F( R )) of F(R) R ) and the line graph L (F 2 ( R )) of F2(R). 2 ( R ) . All finite commutative rings whose genus of L (F( R )) and L (F 2 ( R )) are 0, 1, 2 are completely characterized, respectively.
引用
收藏
页码:1075 / 1084
页数:10
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