Results 21 to 30 of about 7,761,342 (163)
On the Total Double Roman Domination [PDF]
IEEE Access, 2019 Let G = (V, E) be a simple graph. A double Roman dominating function (DRDF) on G is a function f from the vertex set V of G into {0, 1, 2, 3} such that if f (u) = 0, then u must have at least two neighbors assigned 2 or one neighbor assigned 3 under f ...
Zehui Shao +3 more
doaj +3 more sources
Global total Roman domination in graphs
Discrete Mathematics, Algorithms and Applications, 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] for which [Formula: see text] and (ii) the subgraph of [Formula: see text] induced by the set of all ...
Jafar Amjadi +2 more
openaire +3 more sources
Total Roman domination in the lexicographic product of graphs [PDF]
Discrete Applied Mathematics, 2019 A total Roman dominating function of a graph $G=(V,E)$ is a function $f: V(G)\to \{0,1,2\}$ such that for every vertex $v$ with $f(v)=0$ there exists a vertex $u$ adjacent to $v$ with $f(u)=2$, and such that the subgraph induced by the set of vertices labeled one or two has no isolated vertices.
Nicolás Campanelli, Dorota Kuziak
openaire +3 more sources
Total Roman Domination Number of Rooted Product Graphs [PDF]
Mathematics, 2020 Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has ...
Abel Cabrera Martínez +3 more
doaj +2 more sources
Quasi total double Roman domination in graphs
AKCE International Journal of Graphs and CombinatoricsA quasi total double Roman dominating function (QTDRD-function) on a graph [Formula: see text] is a function [Formula: see text] having the property that (i) if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w
S. Kosari +4 more
doaj +2 more sources
Outer-independent total Roman domination in graphs [PDF]
Discrete Applied Mathematics, 2019 Given a graph $G$ with vertex set $V$, a function $f:V\rightarrow \{0,1,2\}$ is an outer-independent total Roman dominating function on $G$ if \begin{itemize} \item every vertex $v\in V$ for which $f(v)=0$ is adjacent to at least one vertex $u\in V$ such that $f(u)=2$, \item every vertex $x\in V$ for which $f(x)\ge 1$ is adjacent to at least one vertex
Abel Cabrera Martínez +2 more
openaire +3 more sources
Signed total strong Roman domination in graphs [PDF]
Discrete Mathematics Letters, 2022 Maryam Hajjari +1 more
doaj +2 more sources
Signed total Roman $k$-domination in directed graphs
Communications in Combinatorics and Optimization, 2016 Let $D$ be a finite and simple digraph with vertex set $V(D)$. A signed total Roman $k$-dominating function (STR$k$DF) on $D$ is a function $f:V(D)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\in N^{-}(v)}f(x)\ge k ...
N. Dehgard, L. Volkmann
doaj +2 more sources
Signed total double Roman dominating functions in graphs
AKCE International Journal of Graphs and CombinatoricsA signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] has at least two neighbors assigned 2 under f or one neighbor w
L. Shahbazi +2 more
doaj +2 more sources
Total Roman Reinforcement in Graphs [PDF]
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
doaj +2 more sources