Results 71 to 80 of about 1,279 (174)

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  

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
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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

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

Total Weak Roman Domination in Graphs [PDF]

, 2019
Given a graph G = ( V , E ) , a function f : V → { 0 , 1 , 2 , ⋯ } is said to be a total dominating function if ∑ u ∈ N ( v ) f ( u ) > 0 for every v ∈ V , where N ( v ) denotes the open ...
Juan A. Rodríguez-Velázquez, Abel Cabrera Martínez, Luis P. Montejano   +2 more
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Roman domination in graphs [PDF]

, 2000
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.Theweight of a Roman dominating function is the value f(V) =
S. T. Hedetniemi, P. A. Dreyer, S. M. Hedetniemi, E. J. Cockayne   +3 more
core  

Perfect roman domination in regular graphs [PDF]

, 2018
A perfect Roman dominating function 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 exactly one vertex v for which f(v) = 2.
Michael Henning, Klostermeyer, William F., Henning, Michael A., William Klostermeyer   +3 more
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Total roman domination in digraphs [PDF]

, 2021
Let D be a nite and simple digraph with vertex set V (D). A Roman dominating function (RDF) on a digraph D is a function f : V (D) → {0; 1; 2} satisfying the condition that every vertex v with f(v) = 0 has an in-neighbor u with f(u) = 2. The weight of an
Zhuang, Wei, Hu, Kangxiu, Hao, Guoliang
core  

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

Independent Roman domination and 2-independence in trees [PDF]

, 2018
Let [Formula: see text] be a simple graph with vertex set [Formula: see text] and edge set [Formula: see text]. A Roman dominating function on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex ...
N. Dehgardi, J. Amjadi, S. M. Sheikholeslami, M. Valinavaz   +3 more
core   +1 more source