On co-maximal subgroup graph of Dn

Let G be a group and S be the collection of all non-trivial proper subgroups of G. The co-maximal subgroup graph Gamma(G) of a group G is defined to be a graph with S as the set of vertices and two distinct vertices H and K are adjacent if and only if HK = G. In this paper, we study the comaximal subgroup graph on finite dihedral groups. In particular, we study order, maximum and minimum degree, diameter, girth, domination number, chromatic number and perfectness of comaximal subgroup graph of dihedral groups. Moreover, we prove some isomorphism results on comaximal subgroup graph of dihedral groups.