Results 31 to 40 of about 8,468 (237)
Remarks on the outer-independent double Italian domination number [PDF]
Opuscula Mathematica, 2021 Let \(G\) be a graph with vertex set \(V(G)\). If \(u\in V(G)\), then \(N[u]\) is the closed neighborhood of \(u\). An outer-independent double Italian dominating function (OIDIDF) on a graph \(G\) is a function \(f:V(G)\longrightarrow \{0,1,2,3\}\) such
Lutz Volkmann
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On Independent Domination in Direct Products
Graphs and Combinatorics, 2022 In \cite{nr-1996} Nowakowski and Rall listed a series of conjectures involving several different graph products. In particular, they conjectured that $i(G\times H) \ge i(G)i(H)$ where $i(G)$ is the independent domination number of $G$ and $G\times H$ is the direct product of graphs $G$ and $H$.
Kirsti Kuenzel, Douglas F. Rall
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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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Independent dominating sets in planar triangulations
Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications, 2023 In 1996, Matheson and Tarjan proved that every planar triangulation on \(n\) vertices contains a dominating set %, i.e., a set \(S\) that contains a neighbor of every vertex not in \(S\), of size at most \(n/3\), and conjectured that this upper bound can be reduced to \(n/4\) when $n$ is sufficiently large.
Botler, Fábio +2 more
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Independent 2-point set domination in graphs - II
AKCE International Journal of Graphs and Combinatorics, 2022 A set D of vertices in a connected graph G is said to be an independent 2-point set dominating set (or in short i-2psd set) of G if D is an independent set and for every non-empty subset [Formula: see text] there exists a non-empty subset [Formula: see ...
Deepti Jain, Purnima Gupta
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Isolate and independent domination number of some classes of graphs
AKCE International Journal of Graphs and Combinatorics, 2019 In this paper we compute isolate domination number and independent domination number of some well known classes of graphs. Also a counter example is provided, which disprove the result on independent domination for Euler Totient Cayley graph proved by ...
Shilpa T. Bhangale, Madhukar M. Pawar
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Theory and Applications of GraphsA graph $G$ is \emph{strongly $i$-bicritical} if it has independent domination number $i(G) \geq 3$, and $i(G - \{x, y\}) = i(G) - 2$ whenever $x$ and $y$ are two non-adjacent vertices of $G$.
Michelle Edwards +2 more
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Independent Roman Domination Stable and Vertex-Critical Graphs
IEEE Access, 2018 A Roman dominating function (RDF) on a graph $G$ is a function $f: V(G) \rightarrow \{0, 1, 2\}$ for which every vertex assigned 0 is adjacent to a vertex assigned 2. The weight of an RDF is the value $\omega (f) = \sum _{u \in V(G)}f(u)$ .
Pu Wu +5 more
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Double Domination and Regular Domination in Intuitionistic Fuzzy Hypergraph
Journal of Mathematics, 2022 This study investigates the domination, double domination, and regular domination in intuitionistic fuzzy hypergraph (IFHG), which has enormous application in computer science, networking, chemical, and biological engineering.
P. Aruna Sri +3 more
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Independent strong domination in complementary prisms
Electronic Journal of Graph Theory and Applications, 2020 Let G = (V, E) be a graph and u,v ∈ V. Then, u strongly dominates v if (i) uv ∈ E and (ii) deg(u) ≥ deg(v). A set D ⊂ V is a strong-dominating set of G if every vertex in V-D is strongly dominated by at least one vertex in D.
Zeynep Nihan Berberler +1 more
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