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Graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set [PDF]
Opuscula MathematicaA graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. We give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield ...
Teresa W. Haynes, Michael A. Henning
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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
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The $k$-Dominating Graph [PDF]
, 2013 Given a graph $G$, the $k$-dominating graph of $G$, $D_k(G)$, is defined to be the graph whose vertices correspond to the dominating sets of $G$ that have cardinality at most $k$.
Haas, Ruth, Seyffarth, Karen
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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
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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
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Efficient and Perfect domination on circular-arc graphs [PDF]
, 2015 Given a graph $G = (V,E)$, a \emph{perfect dominating set} is a subset of vertices $V' \subseteq V(G)$ such that each vertex $v \in V(G)\setminus V'$ is dominated by exactly one vertex $v' \in V'$.
Lin, Min Chih +2 more
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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
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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.
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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.
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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
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