ON EQUALITY IN AN UPPER BOUND FOR DOMINATION PARAMETERS OF GRAPHS

We consider the well-known upper bounds mu(G) less than or equal to \V (G)\ - Delta(G), where Delta(G) denotes the maximum degree of G and mu (G) the irredundance, domination or independent domination numbers of G and give necessary and sufficient conditions for equality to hold in each case. We also describe specific classes of graphs for which equa lity does or does not hold and show that the difference between the do mination and irredundance numbers can be arbitrary even when equality in the above bound holds for the domination number. (C) 1997 John Wile y & Sons, Inc.