• FRACTIONAL TWIN DOMINATION NUMBER IN DIGRAPHS

Abstract

Let D = (V, A) be any digraph. A function : V  [0, 1] is called a twin dominating function (TDF) if the sum of its function values over any closed out-neighborhood is at least one as well as the sum of its function values over any closed in-neighborhood is at least one. A TDF of D is called a minimal TDF if there is no TDF of D such that for all and for some . The weight of the function is = . The fractional twin domination number of D, denoted (D), equals the minimum weight of a TDF of D. In this research paper, we proved a necessary and sufficient condition for a TDF to be minimal and found fractional twin domination number for the digraph namely directed cycle. We established some bounds of fractional twin domination number for any digraph and proved that these bounds were sharp. We also proved a necessary and sufficient condition for fractional twin domination number to be n, where there are n vertices of either outdegree 0 or indegree 0.