Irredundance trees of diameter 3

A set D of vertices a graph G=(V,E) is irredundant if each non-isolated vertex G[D] has neighbour in V−D that not adjacent to any other D. The upper irredundance number IR(G) the largest cardinality an G; IR(G)-set IR(G). IR-graph G IR(G)-sets as set, and sets D′ are only can be obtained from by exchanging single for D′. An IR-tree tree. We characterize IR-trees diameter 3 showing these graphs precisely double stars S(2n,2n), i.e., trees joining central two disjoint K1,2n.