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.

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