TY - JOUR
T1 - Variants of the domination number for flower snarks
AU - Burdett, Ryan
AU - Haythorpe, Michael
AU - Newcombe, Alex
PY - 2024/6/6
Y1 - 2024/6/6
N2 - 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.
AB - 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.
KW - Flower
KW - snarks
KW - domination
KW - variants
KW - secure
UR - http://www.scopus.com/inward/record.url?scp=85199562951&partnerID=8YFLogxK
U2 - 10.26493/1855-3974.2710.f3d
DO - 10.26493/1855-3974.2710.f3d
M3 - Article
AN - SCOPUS:85199562951
SN - 1855-3966
VL - 24
JO - Ars Mathematica Contemporanea
JF - Ars Mathematica Contemporanea
IS - 3
M1 - #P3.04
ER -