Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
419949 | Discrete Applied Mathematics | 2013 | 7 Pages |
Abstract
Assume that G=(V,E) is an undirected graph with vertex set V and edge set E. The ball Br(v) denotes the vertices within graphical distance r from v. A subset CâV is called an (r,â¤l)-locating-dominating code of type B if the sets Ir(F)=âvâF(Br(v)â©C) are distinct for all subsets FâVâC with at most l vertices. We give examples of optimal (r,â¤3)-locating-dominating codes of type B in the infinite king grid for all râN+ and prove optimality. The infinite king grid is the graph with vertex set Z2 and edge set {{(x1,y1),(x2,y2)}â£|x1âx2|â¤1,|y1ây2|â¤1}.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Mikko Pelto,