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