In this thesis some of the domination parameters are discussed, such as the domination number, global domination number, outer connected domination number, global outer connected domination number. We discuss some properties of outer connected domination number where for G be a graph then ̃ ( ) ( ) ( ) . Also in this thesis we show an equality of the global domination number of trees with the global domination number as their squares where if diam ( ) then ( ) ( ) but if diam ( ) 2 3 then ( ) ( ) In this thesis we get some bounds for global outer connected domination number where for any G graph ( ) ( ) ̃ ( ). Finally we verify the conditions that for trees that are ̃ ( ) ̃ ( )
