Results 61 to 70 of about 5,939,930 (166)

Roman game domination subdivision number of a graph [PDF]

Transactions on Combinatorics, 2013
A {em Roman dominating function} on a graph $G = (V ,E)$ is a function $f : Vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. The {em weight} of a
Jafar Amjadi, Hossein Karami, Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +3 more
doaj  

On The Total Roman Domination in Trees

Discussiones Mathematicae Graph Theory, 2019
A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by ...
Amjadi Jafar, Sheikholeslami Seyed Mahmoud, Soroudi Marzieh   +2 more
doaj   +1 more source

Triple Roman domination subdivision number in graphs [PDF]

Computer Science Journal of Moldova, 2022
For a graph $G=(V, E)$, a triple Roman domination function is a function $f: V(G)\longrightarrow\{0, 1, 2, 3, 4\}$ having the property that for any vertex $v\in V(G)$, if $f(v)
Jafar Amjadi, Hakimeh Sadeghi
doaj  

On the upper Bound of double Roman dominating function

, 2019
A double Roman Dominating function on a graph $G$ is a function $ f:V\rightarrow \{0,1,2,3\}$ such that the following conditions hold. If $f(v)=0$, then vertex $v$ must have at least two neighbors in $V_2$ or one neighbor in $V_3$ and if $f(v)=1$, then vertex $v$ must have at least one neighbor in $V_2\bigcup V_3$.
Teimourzadeh, Atieh, Mojdeh, Doost Ali
openaire   +2 more sources

Signed Total Roman Edge Domination In Graphs

Discussiones Mathematicae Graph Theory, 2017
Let G = (V,E) be a simple graph with vertex set V and edge set E. A signed total Roman edge dominating function of G is a function f : Ʃ → {−1, 1, 2} satisfying the conditions that (i) Ʃe′∈N(e) f(e′) ≥ 1 for each e ∈ E, where N(e) is the open ...
Asgharsharghi Leila, Sheikholeslami Seyed Mahmoud   +1 more
doaj   +1 more source

Total Modern Roman Dominating Functions in Graphs

European Journal of Pure and Applied Mathematics
Let $G=(V(G), E(G))$ 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 $f(w)=3$; andfor each $v\in V(G)$ with $f(v)=1$, there exists $u \in N_G (v)$ such that $f(u)=2$ or $f(u)=3$.
Sherihatha Ahamad, Jerry Boy Cariaga, Sheila Menchavez, Ferdinand Jamil   +3 more
openaire   +1 more source

Roman domination in graphs [PDF]

, 2003
A Roman dominating function on a graph G=(V,E) is a function f:V→{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.
Paul A Dreyer, Ernie J Cockayne, Sandra M Hedetniemi, Stephen T Hedetniemi, Hedetniemi, Sandra M, Cockayne, Ernie J, Dreyer, Paul A, Hedetniemi, Stephen T   +7 more
core   +1 more source

Connected Roman Hop Dominating Functions in Graphs

European Journal of Pure and Applied Mathematics
Let $G$ be a connected graph. A hop Roman dominating function $f:V(G)\to \{0,1,2\}$ is a connected hop Roman dominating function (CHRDF) on $G$ if the set $\{u\in V(G): f(u)\neq 0\}$ induces a connected subgraph of $G$. The of weight of a CHRDF f is given by $\omega_G^{cRh}(f)=\sum_{v\in V(G)}f(v)$ and the minimum weight among all connected hop Roman ...
Alkajim Aradais, Jerry Boy Cariaga, Sergio Canoy, Jr.   +2 more
openaire   +1 more source

On The Roman Domination Stable Graphs

Discussiones Mathematicae Graph Theory, 2017
A Roman dominating function (or just RDF) on a graph G = (V,E) is a function f : V → {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.
Hajian Majid, Rad Nader Jafari
doaj   +1 more source

Varieties of Roman domination II

AKCE International Journal of Graphs and Combinatorics, 2020
In this work, we continue to survey what has been done on the Roman domination. More precisely, we will present in two sections several variations of Roman dominating functions as well as the signed version of some of these functions.
M. Chellali, N. Jafari Rad, S. M. Sheikholeslami, L. Volkmann   +3 more
doaj   +1 more source