Results 51 to 60 of about 1,279 (174)
, 2016 For a graph G=(V,E), a double Roman dominating function is a function f:V→{0,1,2,3} having the property that if f(v)=0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor with f(w)=3, and if f(v)=1, then vertex v must have ...
Haynes, Teresa W. +2 more
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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 the Unique Response Roman Domination Numbers of Graphs [PDF]
, 2016 Let G be a graph with vertex set V(G). A function f: V(G) → {0, 1, 2} with the ordered partition (V0, V1, V2) of V(G), where Vi = {V∈V(G) | f(V) = i} for i = 0, 1, 2, is a Roman dominating function if x ∈ V0 implies |N(x)∩V2|≥ 1. It is a unique response
Jian He +4 more
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, 2011 A Roman dominating function on a graph G is a function f:V(G) → {0,1,2} 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. The weight of a Roman dominating function is the value $f(V(G)
Rad, Nader Jafari +2 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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Total Roman {3}-domination in Graphs [PDF]
, 2020 For a graph G = ( V , E ) with vertex set V = V ( G ) and edge set E = E ( G ) , a Roman { 3 } -dominating function (R { 3 } -DF) is a function f : V ( G ) → { 0 , 1 , 2 , 3 } having the property that
Doost Ali Mojdeh +2 more
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Some progress on the mixed roman domination in graphs [PDF]
, 2021 Let G = (V, E) be a simple graph with vertex setxs V and edge set E. A mixed Roman dominating function of G is a function f : V ∪ E → {0, 1, 2} satisfying the condition that every element x ∈ V ∪ E for which f(x) = 0 is adjacent or incident to at least ...
Mustapha Chellali +5 more
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Effect of vertex deletion on the weak Roman domination number of a graph
AKCE International Journal of Graphs and Combinatorics, 2019 Let be a graph and be a function. The weight of a vertex is and a vertex with weight is said to be undefended with respect to , if it is not adjacent to a vertex with positive weight. The function is a weak Roman dominating function (WRDF) if each vertex
P. Roushini Leely Pushpam, M. Kamalam
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