Results 161 to 170 of about 820 (190)

Trees with equal Roman {2}-domination number and independent Roman {2}-domination number

RAIRO - Operations Research, 2019
A Roman {2}-dominating function (R{2}DF) 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 either at least one vertex v with f(v) = 2 or two vertices v1, v2 with f(v1) = f(v2) = 1. The weight of an R{2}DF f is the value w(f) = ∑u∈Vf(u).
Pu Wu   +3 more
openaire   +1 more source

Bounds on the signed total Roman 2-domination in graphs

Discrete Mathematics, Algorithms and Applications, 2020
Let [Formula: see text] be an integer and [Formula: see text] be a simple and finite graph with vertex set [Formula: see text]. A signed total Roman [Formula: see text]-dominating function (STR[Formula: see text]DF) on a graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text ...
R. Khoeilar   +3 more
openaire   +2 more sources

On the computational complexity of Roman$$\{2\}$$-domination in grid graphs

Journal of Combinatorial Optimization, 2023
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Aflatoun Amouzandeh, Ahmad Moradi
openaire   +1 more source

Algorithmic aspects of total Roman \(\{2\}\)-domination in graphs

2021
Summary: For a simple, undirected, connected graph \(G\), a function \(h : V \rightarrow \{0,1,2\}\) is called a total Roman \(\{2\}\)-dominating function (TR2DF) if for every vertex \(v \in V\) with weight 0, either there exists a vertex \(u\) in \(N_G(v)\) with weight 2, or at least two vertices \(x\), \(y\) in \(N_G(v)\) each with weight 1, and the ...
P, Chakradhar, P, Venkata Subba Reddy
openaire   +1 more source

(Independent) Roman {2}-Domination Number on Graphs

Journal of Interconnection Networks
For a graph [Formula: see text], a function [Formula: see text] is a Roman {2}-dominating function (R{2}DF) if [Formula: see text] satisfies the following condition: if [Formula: see text] then there is [Formula: see text] such that [Formula: see text] or there is [Formula: see text] such that [Formula: see text]. Let [Formula: see text] denote the set
Yulan Hu, Luyao Yang, Weihua Yang
openaire   +1 more source

An Upper Bound on the Total Roman { 2 } -domination Number of Graphs with Minimum Degree Two

Journal of Combinatorial Mathematics and Combinatorial Computing
A total Roman \(\{2\}\)-dominating function on a graph \(G = (V,E)\) is a function \(f:V\rightarrow\{0,1,2\}\) with the properties that (i) for every vertex \({v}\in V\) with \(f({v})=0\), \(f(N({v}))\ge2\) and (ii) the set of vertices with \(f({v})>0\) induces a subgraph with no isolated vertices.
Kheibari, M.   +3 more
openaire   +2 more sources

On the Algorithmic Complexity of Roman $$\{2\}$$-Domination (Italian Domination)

Iranian Journal of Science and Technology, Transactions A: Science, 2020
Abolfazl Poureidi, Nader Jafari Rad
openaire   +1 more source

Double Roman Domination: A Survey

Mathematics, 2023
Darja Rupnik Poklukar, Janez Žerovnik
exaly  

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