Results 11 to 20 of about 273,507 (170)
DOMINATION AND EDGE DOMINATION IN TREES [PDF]
Ural Mathematical Journal, 2020 Let \(G=(V,E)\) be a simple graph. A set \(S\subseteq V\) is a dominating set if every vertex in \(V \setminus S\) is adjacent to a vertex in \(S\). The domination number of a graph \(G\), denoted by \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\). A set \(D \subseteq E\) is an edge dominating set if every edge in \(E\setminus D\)
B. Senthilkumar +2 more
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Domination versus edge domination [PDF]
Discrete Applied Mathematics, 2020 We propose the conjecture that the domination number $γ(G)$ of a $Δ$-regular graph $G$ with $Δ\geq 1$ is always at most its edge domination number $γ_e(G)$, which coincides with the domination number of its line graph. We prove that $γ(G)\leq \left(1+\frac{2(Δ-1)}{Δ2^Δ}\right)γ_e(G)$ for general $Δ\geq 1$, and $γ(G)\leq \left(\frac{7}{6}-\frac{1}{204 ...
Julien Baste +4 more
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Dominating Sets and Domination Polynomials of Paths [PDF]
International Journal of Mathematics and Mathematical Sciences, 2009 Let G = (V, E) be a simple graph. A set S⊆V is a dominating set of G, if every vertex in V\S is adjacent to at least one vertex in S. Let be the family of all dominating sets of a path Pn with cardinality i, and let . In this paper, we construct , and obtain a recursive formula for d(Pn, i).
Saeid Alikhani, Yee-Hock Peng
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Domination and Fractional Domination in Digraphs
The Electronic Journal of Combinatorics, 2018 In this paper, we investigate the relation between the (fractional) domination number of a digraph $G$ and the independence number of its underlying graph, denoted by $\alpha(G)$. More precisely, we prove that every digraph $G$ on $n$ vertices has fractional domination number at most $2\alpha(G)$ and domination number at most $2\alpha(G) \cdot \log{n}$.
Harutyunyan, Ararat +3 more
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The Electronic Journal of Combinatorics, 2012 In this paper, we propose a new network reliability measure for some particular kind of service networks, which we refer to as domination reliability. We relate this new reliability measure to the domination polynomial of a graph and the coverage probability of a hypergraph.
Klaus Dohmen, Peter Tittmann 0001
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Domination in functigraphs [PDF]
Discussiones Mathematicae Graph Theory, 2012 Let $G_1$ and $G_2$ be disjoint copies of a graph $G$, and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup \{uv \mid u \in V(G_1), v \in V(G_2), v=f(u)\}$.
Linda Eroh +4 more
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Relating domination, exponential domination, and porous exponential domination
Discrete Optimization, 2017 The domination number $γ(G)$ of a graph $G$, its exponential domination number $γ_e(G)$, and its porous exponential domination number $γ_e^*(G)$ satisfy $γ_e^*(G)\leq γ_e(G)\leq γ(G)$. We contribute results about the gaps in these inequalities as well as the graphs for which some of the inequalities hold with equality.
Michael A. Henning +2 more
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Hereditary equality of domination and exponential domination
Discussiones Mathematicae Graph Theory, 2018 We characterize a large subclass of the class of those graphs $G$ for which the exponential domination number of $H$ equals the domination number of $H$ for every induced subgraph $H$ of $G$.
Michael A. Henning +2 more
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DOMINATION AND REGULARITY [PDF]
The Bulletin of Symbolic Logic, 2020 AbstractWe discuss the close relationship between structural theorems in (generalized) stability theory, and graph regularity theorems.
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Dynamic Functional Connectivity of Emotion Processing in Beta Band with Naturalistic Emotion Stimuli
Brain Sciences, 2022 While naturalistic stimuli, such as movies, better represent the complexity of the real world and are perhaps crucial to understanding the dynamics of emotion processing, there is limited research on emotions with naturalistic stimuli. There is a need to
Sudhakar Mishra +2 more
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