An Archimedean lattice is an infinite graph constructed from a vertex-transitive tiling of the plane by regular polygons. A dominating set of vertices is a perfect dominating set if every vertex that is not in the set is dominated exactly once. The perfect domination ratio is the minimum proportion of vertices in a perfect dominating set. Seven of the eleven Archimedean lattices can be efficiently dominated, which easily determines their perfect domination ratios. The perfect domination ratios are determined for the four Archimedean lattices that can not be efficiently dominated.
@article{10_37236_10210,
author = {Yunfan Zhao and John C Wierman and Thomas G. Marge},
title = {Perfect domination ratios of {Archimedean} lattices},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {3},
doi = {10.37236/10210},
zbl = {1498.05215},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10210/}
}
TY - JOUR
AU - Yunfan Zhao
AU - John C Wierman
AU - Thomas G. Marge
TI - Perfect domination ratios of Archimedean lattices
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/10210/
DO - 10.37236/10210
ID - 10_37236_10210
ER -
%0 Journal Article
%A Yunfan Zhao
%A John C Wierman
%A Thomas G. Marge
%T Perfect domination ratios of Archimedean lattices
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10210/
%R 10.37236/10210
%F 10_37236_10210
Yunfan Zhao; John C Wierman; Thomas G. Marge. Perfect domination ratios of Archimedean lattices. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10210
