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

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.