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Zhejiang Daxue xuebao. Lixue banA Roman dominating function of a graph G is a function f from the vertex set V of G to the set {0,1,2} if the open neighbor of any vertex v of G with f (v)=0 has at least one vertex u with f (u)=2.
谢智红(XIE Zhihong) +3 more
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Outer-Connected Semitotal Double Roman Dominating Function in Graphs.
In this paper, we establish the study of outer-connected semitotal double Roman domination. A function f is said to be an outer-connected semitotal double Roman dominating function of a graph G if it is a double dominating function and satisfies the ...
>Alkajim Aradais
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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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Total Roman Reinforcement in Graphs
Discussiones Mathematicae Graph Theory, 2019 A total Roman dominating function on a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2 and the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex.
Ahangar H. Abdollahzadeh +4 more
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On the $nk-attack Roman Dominating Number of a Graph [PDF]
Given a graph $G=(V,E)$, the dominating number of a graph is the minimum size of a vertex set, $V\u27 \subseteq V$, so that every vertex in the graph is either in $V\u27$ or is adjacent to a vertex in $V\u27$.
Koch, Garrison, Shank, Nathan
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, 2016 For a graph (Formula presented.), a Roman dominating function (Formula presented.) has the property that every vertex (Formula presented.) with (Formula presented.) has a neighbor (Formula presented.) with (Formula presented.).
Haynes, Teresa W. +4 more
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Convex Roman Dominating Functions on Graphs under some Binary Operations
European Journal of Pure and Applied MathematicsLet $G$ be a connected graph. A function $f:V(G)\rightarrow \{0,1,2\}$ is a \textit{convex Roman dominating function} (or CvRDF) if every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$ and $V_1 \cup V_2$ is convex.
Rona Jane Gamayot Fortosa +2 more
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Journal of MathematicsA perfect Roman 3-dominating function on a graph G=V,E is a function f:V⟶0,1,2,3 having the property that if fv=0, then ∑u∈Nvfu=3, and if fv=1, then ∑u∈Nvfu=2 for any vertex v∈V.
Ahlam Almulhim
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On the outer independent total double Roman dominating functions
Let $\{0,1,\dots, t\}$ be abbreviated by $[t].$ A double Roman dominating function (DRDF) on a graph $Γ=(V,E)$ is a map $l:V\rightarrow [3]$ satisfying \textrm{(i)} if $l(r)=0$ then there must be at least two neighbors labeled 2 under $l$ or a neighbor $r'$ with $l(r')=3$; and \textrm{(ii)} if $l(r)=1$ then $r$ must be adjacent to a vertex $r'$ such ...
Ahangar, H. Abdolahzadeh +3 more
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Varieties of Roman domination IV
AKCE International Journal of Graphs and CombinatoricsRoman domination was introduced in 2004 by Cockayne, Dreyer, Hedetniemi, and Hedetniemi. If [Formula: see text] is the vertex set of a graph G, then a function [Formula: see text] is a Roman dominating function if every vertex [Formula: see text] for ...
M. Chellali +3 more
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