ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.)
ARS MATHEMATICA CONTEMPORANEA 24 (2024) #P3.04
https://doi.org/10.26493/1855-3974.2710.f3d
(Also available at http://amc-journal.eu)
Variants of the domination number for flower
snarks
Ryan Burdett, Michael Haythorpe * , Alex Newcombe
Flinders University, 1284 South Road, Tonsley Park, SA, Australia
Received 25 October 2021, accepted 14 July 2023, published online 8 July 2024
Abstract
We consider the flower snarks, a widely studied infinite family of 3–regular graphs. For
the Flower snark Jn on 4n vertices, it is trivial to show that the domination number of Jn is
equal to n. However, results are more difficult to determine for variants of domination. The
Roman domination, weakly convex domination, and convex domination numbers have been
determined for flower snarks in previous works. We add to this literature by determining
the independent domination, 2-domination, total domination, connected domination, upper
domination, secure domination and weak Roman domination numbers for flower snarks.
Keywords: Flower, snarks, domination, variants, secure.
Math. Subj. Class. (2020): 05C69
*Corresponding author.
E-mail addresses: ryan.burdett@flinders.edu.au (Ryan Burdett), michael.haythorpe@flinders.edu.au
(Michael Haythorpe), alex.newcombe@flinders.edu.au (Alex Newcombe)
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 24 (2024) #P3.04
https://doi.org/10.26493/1855-3974.2710.f3d
(Dostopno tudi na http://amc-journal.eu)
Različice dominacijskega števila za rožne snarke
Ryan Burdett, Michael Haythorpe * , Alex Newcombe
Flinders University, 1284 South Road, Tonsley Park, SA, Australia
Prejeto 25. oktobra 2021, sprejeto 14. julija 2023, objavljeno na spletu 8. julija 2024
Povzetek
Obravnavamo rožne snarke, široko raziskano neskončno družino 3–regularnih grafov.
Za rožni snark Jn na 4n točkah je trivialno pokazati, da je dominacijsko število snarka Jn
enako n. Vendar pa je rezultate težje določiti pri različicah dominacije. Števila rimske dom-
inacije, šibko konveksne dominacije in konveksne dominacije so bila določena za rožne
snarke v prejšnjih člankih. To literaturo dopolnjujemo z določitvijo števil neodvisne domi-
nacije, 2-dominacije, totalne dominacije, povezane dominacije, zgornje dominacije, varne
dominacije in šibke rimske dominacije.
Ključne besede: Roža, snarki, dominacija, različice, varno.
Math. Subj. Class. (2020): 05C69
*Kontaktni avtor.
E-poštni naslovi: ryan.burdett@flinders.edu.au (Ryan Burdett), michael.haythorpe@flinders.edu.au
(Michael Haythorpe), alex.newcombe@flinders.edu.au (Alex Newcombe)
cb To delo je objavljeno pod licenco https://creativecommons.org/licenses/by/4.0/