#### Title

A tight lower bound for the split domination number of a regular tournament

#### Document Type

Conference Presentation

#### Department

Mathematics

#### Conference Title

Southeastern International Conference on Combinatorics, Graph Theory & Computing

#### Organization

Florida Atlantic University

#### Location

Boca Raton, FL

#### Conference Dates

March 4-8, 2019

#### Date of Presentation

3-4-2019

#### ISSN

2572-6803

#### Abstract

In a strongly connected digraph, we consider the problem of finding a set of minimum size that is both dominating and separating. A set of vertices, S, is dominating provided for all v in the digraph, either v ∈ S or (w, v) ∈ A(D) for some w ∈ S. In a strongly connected digraph, a set of vertices is separating provided removing this set of vertices results in a digraph that is not strongly connected. Let D be a strongly connected digraph. Then γs(D) denotes the minimum size of a subset of V (D) that is both dominating and separating. We present a tight lower bound for γs(T) where T is a regular tournament.

#### Recommended Citation

Factor, K.,
Langley, L. J.,
&
Merz, S.
(2019).
A tight lower bound for the split domination number of a regular tournament.
Paper presented at Southeastern International Conference on Combinatorics, Graph Theory & Computing in Boca Raton, FL.

https://scholarlycommons.pacific.edu/cop-facpres/1224