Peter J. Slater

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In large organizations there is frequently a need to pass information from one place, e.g., the president’s office or company headquarters, to all other divisions, departments or employees. This is often done along organizational reporting lines. Insofar ,as most organizations are structured in a hierarchical or treelike fashion, this can be described as a(More)
For a graph G that models a facility, various detection devices can be placed at the vertices so as to identify the location of an intruder such as a thief or saboteur. Here we introduce the open neighborhood locating-dominating set problem. We seek a minimum cardinality vertex set S with the property that for each vertex v its open neighborhood N(v) has a(More)
For S E V(G) the S-center and S-centroid of G are defined as the collection of vertices u E V(G) that minimize eJu) = max {d(u, v ) : V E S} and &(u) =IveS d(u, v), respectively. This generalizes the standard definition of center and centroid from the.special case of S = V(G). For 1 s k r ( V ( G ) I and U E V ( G ) let rk(u)=max(C,,,d(u, s ) : S s V ( G )(More)