Fractional Inverse and Inverse Fractional Domination

Abstract

We examine the inverse domination number of a graph, as well as two reasonable candidates for the fractional analogue of this parameter. We also examine the relations among these and other graph parameters. In particular, we show that both proposed fractional analogues of the inverse domination number are no greater than the fractional independence number. These results establish the fractional analogue of a well-known conjecture about the inverse domination and vertex independence numbers of a graph.