ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.)
ARS MATHEMATICA CONTEMPORANEA 23 (2023) #P1.03
https://doi.org/10.26493/1855-3974.2637.f61
(Also available at http://amc-journal.eu)
Domination type parameters of Pell graphs*
Arda Buğra Özer
Middle East Technical University, Northern Cyprus Campus, Kalkanlı, Güzelyurt,
Mersin 10, Turkey
Elif Saygı
Department of Mathematics and Science Education, Hacettepe University, Ankara, Turkey
Zülfükar Saygı †
Department of Mathematics, TOBB University of Economics and Technology, Ankara,
Turkey
Received 20 May 2021, accepted 7 March 2022, published online 12 September 2022
Abstract
Pell graphs are defined on certain ternary strings as special subgraphs of Fibonacci
cubes of odd index. In this work the domination number, total domination number, 2-
packing number, connected domination number, paired domination number, and signed
domination number of Pell graphs are studied. Using integer linear programming, exact
values and some estimates for these numbers of small Pell graphs are obtained. Further-
more, some theoretical bounds are obtained for the domination numbers and total domina-
tion numbers of Pell graphs.
Keywords: Pell graphs, Fibonacci cube, domination number, integer linear programming.
Math. Subj. Class. (2020): 05C69, 68R10
*This work is partially supported by TÜBİTAK under Grant No. 120F125. The authors are grateful to the
anonymous reviewers for their valuable comments and careful reading.
†Corresponding author.
E-mail addresses: abozer@metu.edu.tr (Arda Buğra Özer), esaygi@hacettepe.edu.tr (Elif Saygı),
zsaygi@etu.edu.tr (Zülfükar Saygı)
cb This work is licensed under https://creativecommons.org/licenses/by/4.0/
ISSN 1855-3966 (tiskana izd.), ISSN 1855-3974 (elektronska izd.)
ARS MATHEMATICA CONTEMPORANEA 23 (2023) #P1.03
https://doi.org/10.26493/1855-3974.2637.f61
(Dostopno tudi na http://amc-journal.eu)
Parametri dominacijskega tipa Pellovih grafov*
Arda Buğra Özer
Middle East Technical University, Northern Cyprus Campus, Kalkanlı, Güzelyurt,
Mersin 10, Turkey
Elif Saygı
Department of Mathematics and Science Education, Hacettepe University, Ankara, Turkey
Zülfükar Saygı †
Department of Mathematics, TOBB University of Economics and Technology, Ankara,
Turkey
Prejeto 20. maja 2021, sprejeto 7. marca 2022, objavljeno na spletu 12. septembra 2022
Povzetek
Pellovi grafi so definirani na določenih ternarnih nizih kot posebni podgrafi Fibonacci-
jevih kock lihega indeksa. V tem članku preučujemo dominacijsko število, skupno dom-
inacijsko število, 2-pakirno število, povezano dominacijsko število, parno dominacijsko
število in predznačeno dominacijsko število Pellovih grafov. Z uporabo celoštevilskega
linearnega programiranja poiščemo natančne vrednosti in nekatere ocene za ta števila majh-
nih Pellovih grafov. Poleg tega poiščemo teoretične meje za dominacijska števila in skupna
dominacijska števila Pellovih grafov.
Ključne besede: Pellovi grafi, Fibonaccijeva kocka, dominacijsko število, celoštevilsko linearno pro-
gramiranje.
Math. Subj. Class. (2020): 05C69, 68R10
*To delo delno podpira TÜBİTAK v okviru donacije št. 120F125. Avtorji so hvaležni recenzentom za njihove
dragocene komentarje in skrbno branje.
†Kontaktni avtor.
E-poštni naslovi: abozer@metu.edu.tr (Arda Buğra Özer), esaygi@hacettepe.edu.tr (Elif Saygı),
zsaygi@etu.edu.tr (Zülfükar Saygı)
cb To delo je objavljeno pod licenco https://creativecommons.org/licenses/by/4.0/