#### Title

Digraphs that satisfy a particular Gallai-type theorem.

#### Poster Number

2

#### Format

Poster Presentation

#### Abstract/Artist Statement

If x is a vertex in a digraph then the outset of x is the set of all vertices toward which x has an arc. The closed outset of a set of vertices is S together with the outset of each vertex in x. A set S is dominating if the closed outset is the vertex set. The lower domination number of a digraph is the smallest size of a dominating set in the digraph. The maximum outdegree of a digraph is the maximum size of an outset of any vertex in the digraph. Preliminary results toward the characterizing digraphs satisfying the property that the sum of the lower domination number and the maximum outdegree of a digraph equals the number of vertices in the digraph are discussed.

#### Location

Pacific Geosciences Center

#### Start Date

26-4-2003 9:00 AM

#### End Date

26-4-2003 5:00 PM

Digraphs that satisfy a particular Gallai-type theorem.

Pacific Geosciences Center

If x is a vertex in a digraph then the outset of x is the set of all vertices toward which x has an arc. The closed outset of a set of vertices is S together with the outset of each vertex in x. A set S is dominating if the closed outset is the vertex set. The lower domination number of a digraph is the smallest size of a dominating set in the digraph. The maximum outdegree of a digraph is the maximum size of an outset of any vertex in the digraph. Preliminary results toward the characterizing digraphs satisfying the property that the sum of the lower domination number and the maximum outdegree of a digraph equals the number of vertices in the digraph are discussed.