Abstract We define the queens (resp., rooks) diameter-separation number to be minimum of pawns for which some placement those on an n × board produces a with graph rooks graph) desired diameter d . determine these numbers small values

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 ...