Fractional restrained domination

Abstract

Let G be a graph with a set of V vertices and a set of E edges. A function [Formula: see text] is called a restrained dominating function (RDF) of G if, for every [Formula: see text] [Formula: see text]. A restrained dominating function f of a graph G is called minimal (MRDF) if, for all functions [Formula: see text] such that [Formula: see text] and g(v) [Formula: see text] f(v) for at least one [Formula: see text] g is not a RDF. The fractional restrained domination number [Formula: see text] is defined as follows: [Formula: see text]: f is an MRDF of G[Formula: see text] where [Formula: see text].