Results 41 to 50 of about 5,939,930 (166)
Restrained roman domination in graphs [PDF]
Transactions on Combinatorics, 2015 A Roman dominating function (RDF) on a graph G = (V,E) is defined to be a function satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. A set S V is a Restrained dominating set if every
Roushini Leely Pushpam +1 more
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Roman dominating influence parameters [PDF]
, 2006 A function f: V (G) → {0,1,2} is a Roman dominating function for a graph G = (V,E) if for every vertex v with f(v) = 0, there exists a vertex w ∈ N(v) with f(w) = 2. Emperor Constantine had the requirement that an army or legion could be sent from its
Peter J. Slater +3 more
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On the complexity of some hop domination parameters
Electronic Journal of Graph Theory and Applications, 2019 A hop Roman dominating function (HRDF) on a graph G = (V, E) is a function f : V → {0, 1, 2} having the property that for every vertex v ∈ V with f(v) = 0 there is a vertex u with f(u) = 2 and d(u, v) = 2. The weight of an HRDF f is the sum of its values
Nader Jafari Rad, Elahe Shabani
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The Distance Roman Domination Numbers of Graphs
Discussiones Mathematicae Graph Theory, 2013 Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k ...
Aram Hamideh +2 more
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The Double Roman Domatic Number of a Digraph
Discussiones Mathematicae Graph Theory, 2020 A double Roman dominating function on a digraph D with vertex set V (D) is defined in [G. Hao, X. Chen and L. Volkmann, Double Roman domination in digraphs, Bull. Malays. Math. Sci. Soc. (2017).] as a function f : V (D) → {0, 1, 2, 3} having the property
Volkmann Lutz
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Total double Roman domination in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:V\rightarrow\{0,1,2,3\}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one ...
Guoliang Hao +2 more
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On outer-convex Roman dominating function in graphs
The American Journal of CombinatoricsLet \(G = (V(G), E(G))\) be a connected graph and let \(\phi:V(G)\rightarrow \{0,1,2\}\) be a Roman dominating function (RDF) on \(G\). For each \(j \in \{0, 1, 2\}\), let \(V_j=\{x \in V(G): \phi(x)=j\}\).
Leomarich Casinillo
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Approximation hardness of dominating set problems in bounded degree graphs [PDF]
, 2008 We study approximation hardness of the Minimum Dominating Set problem and its variants in undirected and directed graphs. Using a similar result obtained by Trevisan for Minimum Set Cover we prove the first explicit approximation lower bounds for various
Chlebikova, Janka +4 more
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On Hop Roman Domination in Trees [PDF]
Communications in Combinatorics and Optimization, 2019 Let $G=(V,E)$ be a graph. A subset $S\subset V$ is a hop dominating set if every vertex outside $S$ is at distance two from a vertex of $S$. A hop dominating set $S$ which induces a connected subgraph is called a connected hop dominating set of $G$.
N. Jafari Rad, A. Poureidi
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Modern Roman Dominating Functions In Graphs
European Journal of Pure and Applied MathematicsLet $G=(V(G), E(G))$ be any connected graph. A function $f:V(G) \to \{0,1,2,3\}$ is a modern Roman dominating function of $G$ if for each $v\in V(G)$ with $f(v)=0$, there exist $u,w \in N_G (v)$ such that $f(u)=2$ and $f(w)=3$; and for each $v\in V(G)$ with $f(v)=1$, there exists $u \in N_G (v)$ such that $f(u)=2$ or $f(w)=3$.
Sherihatha Ahamad +2 more
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