Results 61 to 70 of about 1,279 (174)

The Perfect Roman Domination Number of the Cartesian Product of Some Graphs

Journal of Mathematics, 2022
A perfect Roman dominating function on a graph G is a function f:VG⟶0,1,2 for which every vertex v with fv=0 is adjacent to exactly one neighbor u with fu=2. The weight of f is the sum of the weights of the vertices.
Ahlam Almulhim, Abolape Deborah Akwu, Bana Al Subaiei   +2 more
doaj   +1 more source

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 $f(w)=3$; and for each $v\in V(G)$ with $f(v)=1$, there exists $u \in N_G (v)$ such that $f(u)=2$ or $f(w)=3$.
Sherihatha Ahamad, Jerry Boy G. Cariaga, Sheila M. Menchavez   +2 more
openaire   +1 more source

Lower bounds on the Roman and independent Roman domination numbers [PDF]

, 2016
A Roman dominating function (RDF) on a graph G is a function f : V (G) → (0, 1,2) satisfying the condition that every vertex u with f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2.
Haynes, Teresa W., Stephen Hedetniemi, Mustapha Chellali, Chellali, Mustapha, Teresa Haynes, Hedetniemi, Stephen T.   +5 more
core   +1 more source

Further results on independent double roman trees

AKCE International Journal of Graphs and Combinatorics, 2022
A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v
A. Rahmouni, H. Abdollahzadeh Ahangar, M. Chellali, S. M. Sheikholeslami   +3 more
doaj   +1 more source

The Signed Total Roman k-Domatic Number Of A Graph

Discussiones Mathematicae Graph Theory, 2017
Let k ≥ 1 be an integer. A signed total Roman k-dominating function on a graph G is a function f : V (G) → {−1, 1, 2} such that Ʃu2N(v) f(u) ≥ k for every v ∈ V (G), where N(v) is the neighborhood of v, and every vertex u ∈ V (G) for which f(u) = −1 is ...
Volkmann Lutz
doaj   +1 more source

Extremal Graphs for a Bound on the Roman Domination Number

Discussiones Mathematicae Graph Theory, 2020
A Roman dominating function on a graph G = (V, E) is a function f:V (G) → {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman dominating function is the value w(f) = Σu∈V(G)f(u).
Bouchou Ahmed, Blidia Mostafa, Chellali Mustapha   +2 more
doaj   +1 more source

Roman {2}-Domination [PDF]

, 2016
In this paper, we initiate the study of a variant of Roman dominating functions. For a graph G=(V,E), a Roman {2}-dominating function f:V→{0,1,2} has the property that for every vertex v∈V with f(v)=0, either v is adjacent to a vertex assigned 2 under f,
Haynes, Teresa W., Chellali, Mustapha, Hedetniemi, Stephen T., McRae, Alice A.   +3 more
core   +1 more source

The signed Roman domatic number of a digraph

Electronic Journal of Graph Theory and Applications, 2015
Let $D$ be a finite and simple digraph with vertex set $V(D)$.A {\em signed Roman dominating function} on the digraph $D$ isa function  $f:V (D)\longrightarrow \{-1, 1, 2\}$ such that$\sum_{u\in N^-[v]}f(u)\ge 1$ for every $v\in V(D)$, where $N^-[v ...
Seyed Mahmoud Sheikholeslami, Lutz Volkmann   +1 more
doaj   +1 more source

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