DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

Journal Impact Factor (JIF 2022): 0.7

5-year Journal Impact Factor (2022): 0.7

CiteScore (2022): 1.9

SNIP (2022): 0.902

Discussiones Mathematicae Graph Theory

Article in volume

Authors:

D.J. Klein

Douglas J. Klein

Texas A$\&$M University at Galveston, Foundational Sciences,
Galveston, TX 77553, United States

email: kleind@tamug.edu

0000-0002-5354-0065

J.A. Rodríguez-Velázquez

Juan A. Rodríguez-Velázquez

Universitat Rovira i Virgili, Departament d'Enginyeria Informàtica i Matemàtiques,
Av. Països Catalans 26, 43007 Tarragona, Spain

email: juanalberto.rodriguez@urv.cat

0000-0002-9082-7647

Title:

Protection of lexicographic product graphs

PDF

Source:

Discussiones Mathematicae Graph Theory 42(1) (2022) 139-158

Received: 2019-01-21 , Revised: 2019-08-23 , Accepted: 2019-08-23 , Available online: 2019-10-14 , https://doi.org/10.7151/dmgt.2243

Abstract:

In this paper, we study the weak Roman domination number and the secure domination number of lexicographic product graphs. In particular, we show that these two parameters coincide for almost all lexicographic product graphs. Furthermore, we obtain tight bounds and closed formulas for these parameters.

Keywords:

lexicographic product, weak Roman domination, secure domination, total domination, double total domination

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