On Codes Identifying Vertices in the Two-Dimensional Square Lattice with Diagonals
IEEE Transactions on Computers
On locating-dominating sets in infinite grids
European Journal of Combinatorics
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
Watching systems in graphs: An extension of identifying codes
Discrete Applied Mathematics
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Assume that G=(V,E) is an undirected graph with vertex set V and edge set E. The ball B"r(v) denotes the vertices within graphical distance r from v. A subset C@?V is called an (r,@?l)-locating-dominating code of type B if the sets I"r(F)=@?"v"@?"F(B"r(v)@?C) are distinct for all subsets F@?V@?C with at most l vertices. We give examples of optimal (r,@?3)-locating-dominating codes of type B in the infinite king grid for all r@?N"+ and prove optimality. The infinite king grid is the graph with vertex set Z^2 and edge set {{(x"1,y"1),(x"2,y"2)}||x"1-x"2|@?1,|y"1-y"2|@?1}.