On eternal domination and Vizing-type inequalities

Authors

Keith Driscoll, Clayton State University
William F. Klostermeyer, University of North FloridaFollow
Elliot Krop, Clayton State University
Colton Magnant, Clayton State University
Patrick Taylor, Shelton State Community College

Document Type

Article

Publication Date

1-1-2020

Abstract

We show sharp Vizing-type inequalities for eternal domination. Namely, we prove that for any graphs G and H, (Formula presented.) where (Formula presented.) is the eternal domination function, α is the independence number, and (Formula presented.) is the strong product of graphs. This addresses a question of Klostermeyer and Mynhardt. We also show some families of graphs attaining the strict inequality (Formula presented.) where (Formula presented.) is the Cartesian product. For the eviction model of eternal domination, we show a sharp upper bound for (Formula presented.).

Publication Title

AKCE International Journal of Graphs and Combinatorics

Volume

17

Issue

3

First Page

708

Last Page

712

Digital Object Identifier (DOI)

10.1016/j.akcej.2019.12.013

ISSN

09728600

Citation Information

Driscoll, K., Klostermeyer, W.F., Krop, E., Magnant, C., Taylor, P. (2020) On eternal domination and Vizing-type inequalities. AKCE International Journal of Graphs and Combinatorics, 17(3), 708-712.