Global secure sets of grid-like graphs

Global forcing number of grid graphs

Security number of grid-like graphs

The security number of a graph is the cardinality of a smallest vertex subset of the graph such that any attack on the subset is defendable. In this paper, we determine the security number of two-dimensional cylinders and tori. This result settles a conjecture of Brigham et al. [R.C. Brigham, R.D. Dutton, S.T. Hedetniemi, Security in graphs, Discrete Appl. Math. 155 (2007) 1708–1714]. © 2009 El...

Computing Secure Sets in Graphs using Answer Set Programming

Problems from the area of graph theory always served as fruitful benchmarks in order to explore the performance of Answer Set Programming (ASP) systems. A relatively new branch in graph theory is concerned with so-called secure sets. It is known that verifying whether a set is secure in a graph is already co-NP-hard. The problem of enumerating all secure sets thus is challenging for ASP and its...

The MILS Architecture for a Secure Global Information Grid

H igh-assurance systems are used in environments where failure can cause security breaches or even a loss of life [1]. Examples include avionics, weapon controls, intelligence gathering, and life-support systems. Before such a system can be deployed, there must exist convincing evidence that it can support critical safety as well as security properties. The avionics community has addressed the ...

Counting maximal distance-independent sets in grid graphs

Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any l ∈ N, maximal distance-l independent (or simply: maximal l-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied.