| dc.creator | Fuentes Castilla, Luis R. | |
| dc.creator | Dejter, Italo J. (Consejero) | |
| dc.date | 2017-01-27T18:33:37Z | |
| dc.date | 2017-01-27T18:33:37Z | |
| dc.date | 2015-07-27T18:33:37Z | |
| dc.date.accessioned | 2017-03-17T16:54:54Z | |
| dc.date.available | 2017-03-17T16:54:54Z | |
| dc.identifier | http://hdl.handle.net/10586 /595 | |
| dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/647709 | |
| dc.description | We study efficient dominating sets in the integer lattices as well as some re-
lated topics. In particular, we study the existence of lattice-like tilings of the n-
dimensional integer lattice by the union of a cartesian product of paths and an
isolated vertex and we present two types of these lattice-like tilings. We also study
the existence of lattice-like tilings of the n-dimensional integer lattice by generalized
Lee spheres around cubes of at least two different dimensions. While this was already
known for n = 2, a perfect dominating set for n = 3 is constructed whose induced
components are squares and isolated vertices. In generalizing this, an extension of
the notion of generalized Lee sphere in a graph-theoretical context is given to one of
cube-sphere. A lattice-like cube-sphere tiling of the n-dimensional integer lattice by
the connected union of two generalized Lee spheres of radius 1 around (n−1)-cubes
and two cube-spheres of radius n − 2 around isolated vertices is given. Finally, we
prove that there are not non-lattice-like tiling in the 3-dimensional integer lattice
with squares. | |
| dc.subject | Graph theory | |
| dc.subject | Cube-sphere | |
| dc.subject | Dominating sets | |
| dc.subject | Tilings | |
| dc.title | Perfect Domination and Cube-Sphere Tilings of Zn | |
| dc.type | Tesis | |
