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 unique non-empty intersection with S. ...

In this paper we present two principal results. In Theorem 1 we show that if r¡ denotes the open set of (conservative) matrices which map some subspace of c of infinite deficiency isomorphically onto c and if A denotes the closed set of matrices which sum some bounded divergent sequence, then [r']~=A. In Theorem 2 we produce a class of triangular matrices with the property that no triangular ma...