A DIRECT INDUCTIVE PROOF OF A CONJECTURE DUE TO E-SAMPATHKUMAR AND L PUSHPA LATHA ON THE WEAK DOMINATION NUMBER OF A TREE

A direct inductive proof, which is more illuminating. of a conjecture that the independent domination number of a tree is at most equal to i ts weak domination number (due to Sampathkumar and Pushpa Latha) has b een provided. A more explicit proof has been given that the weak domin ation number of a tree is at most equal to its independence number as well by showing that the two numbers are in fact equal for trees havin g diameter at most four.