Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Discrete Applied Mathematics
Bounds on a graph's security number
Discrete Applied Mathematics
Global defensive alliances in star graphs
Discrete Applied Mathematics
Note: Security number of grid-like graphs
Discrete Applied Mathematics
| Hi-index | 5.23 |
Let G=(V,E) be a graph. A global secure set SD@?V is a dominating set which also satisfies a condition that |N[X]@?SD|=|N[X]-SD| for every subset X@?SD. The minimum cardinality of the global secure set in the graph G is denoted by @c"s(G). In this paper, we introduce the notion of @c"s-monotone graphs. The graph G is @c"s-monotone if, for every k@?{@c"s(G),@c"s(G)+1,...,n}, it has a global secure set of cardinality k. We will also present the results concerning the minimum cardinality of the global secure sets in the class of cographs.