منابع مشابه
Reconfiguration of Dominating Sets
We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph G is a set S of vertices such that each vertex is either in S or has a neighbour in S. In a reconfiguration problem, the goal is to determine whether there exists a sequence of feasible solutions connecting given feasible solutions s and t such that each pair of consecutive solutions is adjacen...
متن کاملThe Complexity of Dominating Set Reconfiguration
Suppose that we are given two dominating sets Ds and Dt of a graph G whose cardinalities are at most a given threshold k. Then, we are asked whether there exists a sequence of dominating sets of G between Ds and Dt such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This problem is k...
متن کاملStrength of strongest dominating sets in fuzzy graphs
A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...
متن کاملConnected Dominating Sets
PROBLEM DEFINITION Consider a graph G = (V,E). A subset C of V is called a dominating set if every vertex is either in C or adjacent to a vertex in C. If, furthermore, the subgraph induced by C is connected, then C is called a connected dominating set. A connected dominating set with a minimum cardinality is called a minimum connected dominating set (MCDS). Computing a MCDS is an NP-hard proble...
متن کاملClique-like Dominating Sets
Continuing work by B acso and Tuza and Cozzens and Kelleher, we investigate dominating sets which induce subgraphs with small clique covering number, or small independence number. We show that if a graph G is connected and contains no induced subgraph isomorphic to P6 or Ht (the graph obtained by subdividing each edge of K1;t; t 3), then G has a dominating set which induces a connected graph wi...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2015
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-015-9947-x