Results 51 to 60 of about 7,400,368 (352)
Weighted Domination of Independent Sets [PDF]
Graphs and Combinatorics, 2019 The {\em independent domination number} $ ^i(G)$ of a graph $G$ is the maximum, over all independent sets $I$, of the minimal number of vertices needed to dominate $I$. It is known \cite{abz} that in chordal graphs $ ^i$ is equal to $ $, the ordinary domination number.
Aharoni, Ron, Gorelik, Irina
openaire +3 more sources
DOMINATING SET ON CHAIN OF FUZZY GRAPHS
Tikrit Journal of Pure Science, 2023 In this paper, we define fuzzy graph chains, which comprise vertex identification. These fuzzy graphs are isomorphic fuzzy graphs, provide that after applying various features to the chain of fuzzy graphs, which as special fuzzy graph chain of .
Russel H. Majeed, Nabeel E. Arif
doaj +1 more source
On the Parameterized Complexity of Approximating Dominating Set
Journal of the ACM, 2019 We study the parameterized complexity of approximating the k-Dominating Set (DomSet) problem where an integer k and a graph G on n vertices are given as input, and the goal is to find a dominating set of size at most F(k) ⋅ k whenever the graph G has a ...
S. KarthikC. +2 more
semanticscholar +1 more source
Lossy Kernels for Connected Dominating Set on Sparse Graphs [PDF]
Symposium on Theoretical Aspects of Computer Science, 2017 Given a graph $G$ and $k\in{\mathbb N}$, the Dominating Set problem asks for a subset $D$ of $k$ vertices such that every vertex in $G$ is either in $D$ or has a neighbor in $D$.
E. Eiben +3 more
semanticscholar +1 more source
Edge Dominating Sets in Graphs [PDF]
SIAM Journal on Applied Mathematics, 1980 We prove that the edge dominating set problem for graphs is $NP$-complete even when restricted to planar or bipartite graphs of maximum degree 3. We show as a corollary that the minimum maximal matching and the achromatic number problems are $NP$-complete.
Yannakakis, M., Gavril, F.
openaire +2 more sources
Domination, Eternal Domination, and Clique Covering
Discussiones Mathematicae Graph Theory, 2015 Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal domination allows one guard to move per attack, whereas more than one guard may move per attack in the m-
Klostermeyer William F., Mynhardt C.M.
doaj +1 more source
Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems
Mathematics, 2019 The minimum connected dominating set (MCDS) problem is a very significant NP-hard combinatorial optimization problem, and it has been used in many fields such as wireless sensor networks and ad hoc networks.
Ruizhi Li +5 more
semanticscholar +1 more source
Some results on domination in annihilating-ideal graphs of commutative rings [PDF]
Journal of Hyperstructures. Let R be a commutative ring with identity and A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A∗(R) = A(R)\{(0)} and two distinct vertices I and J are ...
Reza Taheri
doaj +1 more source
Approximating Minimum Independent Dominating Sets in Wireless Networks [PDF]
, 2007 We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth.
Hurink, J.L., Nieberg, T.
core +6 more sources
Twin-width III: Max Independent Set, Min Dominating Set, and Coloring
International Colloquium on Automata, Languages and ProgrammingWe recently introduced the notion of twin-width, a novel graph invariant, and showed that first-order model checking can be solved in time f ( d, k ) n for n -vertex graphs given with a witness that the twin-width is at most d , called d -contraction ...
Édouard Bonnet +4 more
semanticscholar +1 more source