Joanna Raczek NP - COMPLETENESS OF WEAKLY CONVEX AND CONVEX DOMINATING SET DECISION PROBLEMS
نویسنده
چکیده
The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are NP -complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.
منابع مشابه
Graphs with convex domination number close to their order
For a connected graph G = (V,E), a set D ⊆ V (G) is a dominating set of G if every vertex in V (G)−D has at least one neighbour in D. The distance dG(u, v) between two vertices u and v is the length of a shortest (u− v) path in G. An (u− v) path of length dG(u, v) is called an (u− v)-geodesic. A set X ⊆ V (G) is convex in G if vertices from all (a − b)-geodesics belong to X for any two vertices...
متن کاملThe convex domination subdivision number of a graph
Let $G=(V,E)$ be a simple graph. A set $Dsubseteq V$ is adominating set of $G$ if every vertex in $Vsetminus D$ has atleast one neighbor in $D$. The distance $d_G(u,v)$ between twovertices $u$ and $v$ is the length of a shortest $(u,v)$-path in$G$. An $(u,v)$-path of length $d_G(u,v)$ is called an$(u,v)$-geodesic. A set $Xsubseteq V$ is convex in $G$ ifvertices from all $(a, b)$-geodesics belon...
متن کاملAn algorithm for approximating nondominated points of convex multiobjective optimization problems
In this paper, we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP), where the constraints and the objective functions are convex. We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points. The proposed algorithm can be appl...
متن کاملConvex Generalized Semi-Infinite Programming Problems with Constraint Sets: Necessary Conditions
We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...
متن کاملEfficient Algorithm for the Paired-Domination Problem in Convex Bipartite Graphs
Let G = (V, E) be a graph without isolated vertices. A matching in G is a set of independent edges in G. A perfect matching M in G is a matching such that every vertex of G is incident to an edge of M . A set S ⊆ V is a paired-dominating set of G if every vertex not in S is adjacent to a vertex in S, and if the subgraph induced by S contains a perfect matching. The paired-domination problem is ...
متن کامل