TY - JOUR
T1 - The secure domination number of Cartesian products of small graphs with paths and cycles
AU - Haythorpe, Michael
AU - Newcombe, Alex
PY - 2022/3/15
Y1 - 2022/3/15
N2 - The secure domination numbers of the Cartesian products of two small graphs with paths or cycles is determined, as well as for Möbius ladder graphs. Prior to this work, in all cases where the secure domination number has been determined, the proof has either been trivial, or has been derived from lower bounds established by considering different forms of domination. However, the latter mode of proof is not applicable for most graphs, including those considered here. Hence, this work represents the first attempt to determine secure domination numbers via the properties of secure domination itself, and it is expected that these methods may be used to determine further results in the future.
AB - The secure domination numbers of the Cartesian products of two small graphs with paths or cycles is determined, as well as for Möbius ladder graphs. Prior to this work, in all cases where the secure domination number has been determined, the proof has either been trivial, or has been derived from lower bounds established by considering different forms of domination. However, the latter mode of proof is not applicable for most graphs, including those considered here. Hence, this work represents the first attempt to determine secure domination numbers via the properties of secure domination itself, and it is expected that these methods may be used to determine further results in the future.
KW - Graph
KW - Cycles
KW - Paths
KW - Cartesian product
KW - Secure domination
UR - http://www.scopus.com/inward/record.url?scp=85120312048&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2021.11.008
DO - 10.1016/j.dam.2021.11.008
M3 - Article
SN - 0166-218X
VL - 309
SP - 32
EP - 45
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -