ON MULTIPLE INTRUDER LOCATING DOMINATION IN INFINITE GRIDS

2020 ◽  
Vol 24 (1) ◽  
pp. 1-12
Author(s):  
K. Venugopal ◽  
K. A. Vidya
Keyword(s):  
Infinite Grids

scholarly journals Lower Bounds for Identifying Codes in some Infinite Grids

10.37236/394 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Ryan Martin ◽  
Brendon Stanton
Keyword(s):  
Lower Bounds ◽  
Finite Graph ◽  
Infinite Graphs ◽  
Locally Finite ◽  
Identifying Codes ◽  
Identifying Code ◽  
Hexagonal Grids ◽  
Closed Neighborhood ◽  
Definition Of ◽  
Infinite Grids

An $r$-identifying code on a graph $G$ is a set $C\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood with $C$ is nonempty and unique. On a finite graph, the density of a code is $|C|/|V(G)|$, which naturally extends to a definition of density in certain infinite graphs which are locally finite. We present new lower bounds for densities of codes for some small values of $r$ in both the square and hexagonal grids.

scholarly journals On locating–dominating sets in infinite grids

2006 ◽  
Vol 27 (2) ◽  
pp. 218-227 ◽  
Author(s):  
Iiro Honkala ◽  
Tero Laihonen
Keyword(s):  
Dominating Sets ◽  
Infinite Grids
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