Open neighborhood locating-dominating in trees

Authors:
Suk J. Seo;Peter J. Slater
Affiliations:
Computer Science Department, Middle Tennessee State University, Murfreesboro, TN 37132, USA;Computer Science Department, University of Alabama in Huntsville, Huntsville, AL 35899, USA and Mathematical Sciences Department, University of Alabama in Huntsville, Huntsville, AL 35899, USA
Venue:
Discrete Applied Mathematics
Year:
2011

Citing 5
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Abstract

For a graph G that models a facility or a multiprocessor network, detection devices can be placed at the vertices so as to identify the location of an intruder such as a thief or saboteur or a faulty processor. Open neighborhood locating-dominating sets are of interest when the intruder/fault at a vertex precludes its detection at that location. The parameter OLD(G) denotes the minimum cardinality of a vertex set S@?V(G) such that for each vertex v in V(G) its open neighborhood N(v) has a unique non-empty intersection with S. For a tree T"n of order n we have @?n/2@?+1@?OLD(T"n)@?n-1. We characterize the trees that achieve these extremal values.