Line comaximal graphs

Let R be a commutative ring with non-zero identity. The comaximal graph is a graph with vertices allelements of R and two distinct vertices x and y are adjacent if and only if Rx +Ry = R. Let \Gamma_۲(R) be the subgraph of the comaximal graph with vertex-set W^{*}(R), where W^{*}(R) is the set of all non-zero and non-unit elements of R. In this paper, we investigate when the graph \Gamma_۲(R) is a line graph. We completely present all commutative rings which their comaximal graphs are line graphs. Also, we study when the comaximal graph is the complement of a line graph.

کلیدواژه ها:

comaximal graph ، line graph ، complement of a graph