Double Domination Number of Subgroup Lattice of a Group

Abstract

A subgroup lattice  is a diagram that includes all the subgroups of the  group  and then if  and  are subgroups of  with  and there is no subgroup  such that , then  appear above  and a segment is drawn connecting  and . The graph of subgroups lattice is denoted by . A subset  of  is double dominating set of  if for every vertex , , that is  in  and has at least one neighbour in  or  and has at least two neighbours in . The double domination number  in subgroup lattice  is a minimum cardinality of double dominating set. In this paper some upper and sharp bounds on  are obtained