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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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A note on Roman domination in graphs [PDF]
, 2006 Let G=(V,E) be a simple graph. A subset S⊆V is a dominating set of G, if for any vertex u∈V-S, there exists a vertex v∈S such that uv∈E. The domination number of G, γ(G), equals the minimum cardinality of a dominating set.
Chen, Xin +2 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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Independent double Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2020 For a graph G = (V,E), a double Roman dominating function has the property that for every vertex with f(v) = 0, either there exists a vertex , with f(u) = 3, or at least two neighbors having f(x) = f(y) = 2, and every vertex with value 1 under f has at ...
H. R. Maimani +3 more
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Upper bounds on Roman domination numbers of graphs [PDF]
, 2012 A Roman dominating function of a graph G is a function f:V(G)→{0,1,2} such that whenever f(v)=0 there exists a vertex u adjacent to v with f(u)=2. The weight of f is w(f)=∑v∈V(G)f(v).
Liu, Chun-Hung, Chang, Gerard Jennhwa
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Global total Roman domination in graphs [PDF]
, 2017 A total Roman dominating function (TRDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the conditions (i) every vertex [Formula: see text] for which [Formula: see text] is adjacent at least one vertex [Formula: see text ...
J. Amjadi +2 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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Mixed Roman Domination in Graphs [PDF]
, 2017 Let G= (V, E) be a simple graph with vertex set V and edge set E. A mixed Roman dominating function (MRDF) of G is a function f: V∪ E→ { 0 , 1 , 2 } satisfying the condition every element x∈ V∪ E for which f(x) = 0 is adjacent or incident to at least one
Haynes, Teresa W. +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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