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 (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 ₂ (R) be a subgraph of (R) induced by R\U (R) J (R) \. In this paper, we investigate the genus of the line graph L ( (R) ) of (R) and the line graph L (₂ (R) ) of ₂ (R). All finite commutative rings whose genus of L ( (R) ) and L (₂ (R) ) are 0, 1, 2 are completely characterized, respectively.