Since every

acyclic digraph has a vertex of indegree 0, B([[LAMBDA].sub.*] - [I.sub.l]) has a zero column, say i-th one.

However, the new approach in their work is mixing the concept of the reflexive

acyclic digraph with fixed point results.

Then, M is the double competition multigraph of an

acyclic digraph if and only if there exist an ordering ([v.sub.1],..., [v.sub.n]) of the vertices ofM and a double indexed edge clique partition {[S.sub.ij] | i, j [member of] [n]} of M such that the following conditions hold:

Acyclic Digraph. A directed graph is graph G, that is, a set of objects (called vertices or nodes) that are connected together, where all the edges are directed from one vertex to another.

If D is an

acyclic digraph, then respecting intervals means preserving the partial order induced by D.

An activity network is an

acyclic digraph, where the vertices represent events, and the direct edges represent the activities, to be performed in a project [1,2].

The running of process phases is subject to precedence restrictions whose there is associated the

acyclic digraph G = (F,U), where if x, y [member of] F, then (x, y) [member of] U if and only if the beginning of the phase y need finishing of phase x.

The running of process phases is subject to precedence restrictions whose there is associated the

acyclic digraph G = (F, U), where if x, y [member of] F, then (x, y) [member of] U if and only if the beginning of the phase y need finishing of phase x.

A DAP (directed acyclic partition) is a pair [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [pi] is a set partition, and [??] is an

acyclic digraph with vertex set given by the blocks of [pi].

For illustration, recall that a vertex subset S [subset or equal to] V of a digraph G is a directed feedback vertex set, if removing S from G leaves an

acyclic digraph. Off the cuff, we can devise an exact algorithm for minimum directed feedback vertex set on sparse digraphs.

Roberts [12] observed that any graph G together with sufficiently many isolated vertices is the competition graph of an

acyclic digraph. The competition number k(G) of a graph G is defined to be the smallest nonnegative integer k such that G together with k isolated vertices added is the competition graph of an

acyclic digraph.

Indeed, a network whose underlying interaction graph is an

acyclic digraph can only eventually end up in a configuration that will never change over time (aka.