Results 171 to 180 of about 302 (207)
Some of the next articles are maybe not open access.
Roman game domination number of a graph
Journal of Combinatorial Optimization, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Bahremandpour +2 more
openaire +2 more sources
On the double Roman domination number in trees [PDF]
Australas. J Comb., 2020 Summary: For a graph \(G\), let \(\gamma_{dR}(G)\) and \(\gamma_R(G)\) denote the double Roman domination number and the Roman domination number, respectively. In this paper, we show that for every tree \(T\) of order \(n\geq 3\), with \(\ell(T)\) leaves and \(s(T)\) support vertices, \begin{align*} \gamma_R(T)+\lceil & \frac{\ell(T)-s(T)}{\Delta(T ...
Sakineh Nazari-Moghaddam +1 more
openaire +1 more source
DOUBLE ROMAN DOMINATION NUMBER OF MIDDLE GRAPH
South East Asian J. of Mathematics and Mathematical Sciences, 2022For any graph G(V, E), a function f : V (G) 0, 1, 2, 3 is called Double Roman dominating function (DRDF) if the following properties holds, If f (v) = 0, then there exist two vertices v1, v2 ∈ N (v) for which f (v1) = f (v2) = 2 or there exist one vertex u ∈ N (v) for which f (u) = 3.∈ If f (v) = 1, then there exist one vertex u N (v) for which
Shirkol, Shailaja S. +2 more
openaire +2 more sources
The generous Roman domination number
2023Summary: Let \(G = (V, E)\) be a simple graph and \(f: V\rightarrow\{0, 1, 2, 3\}\) be a function. A vertex \(u\) with \(f(u) = 0\) is called an undefended vertex with respect to \(f\) if it is not adjacent to a vertex \(v\) with \(f(v) \geq 2\). We call the function \(f\) a generous Roman dominating function (GRDF) if for every vertex with \(f(u) = 0\)
Mohammed, Benatallah +2 more
openaire +1 more source
Note on the perfect Roman domination number of graphs
Applied Mathematics and Computation, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun Yue 0002, Jiamei Song
openaire +2 more sources
A note on Roman \(k\)-tuple domination number
2021Summary: For an integer \(k \geq 2\), a Roman \(k\)-tuple dominating function, (or just R\(k\)DF), in a graph \(G\) is a function \(f:V(G) \rightarrow \{0, 1, 2\}\) satisfying the condition that every vertex \(u\) for which \(f(u) = 0\) is adjacent to at least \(k\) vertices \(v\) for which \(f(v) = 2\), and every vertex \(u\) for which \(f(u) \neq 0\)
Jafari Rad, Nader, Aziz, Noor
openaire +2 more sources
Trees with independent Roman domination number twice the independent domination number
Discrete Mathematics, Algorithms and Applications, 2015A Roman dominating function (RDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] for which [Formula: see text] is adjacent to at least one vertex [Formula: see text] for which [Formula: see text].
Mustapha Chellali, Nader Jafari Rad
openaire +2 more sources
Roman Domination and Double Roman Domination Numbers of Sierpiński Graphs $$S(K_n,t)$$
Bulletin of the Malaysian Mathematical Sciences Society, 2021Sierpiński graph \(S_n^t\) can be defined recursively as \(S_n^1\cong K_n\) and one obtains \(S_n^{t+1}\) from \(S_n^t\) by replacing each vertex from \(S_n^t\) by a copy of \(K_n\) and adding some special edges between these copies of \(K_n\). Let \(G\) be a graph.
openaire +2 more sources
Bounds on weak roman and 2-rainbow domination numbers
Discrete Applied Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
TERESA W Haynes, Stephen T Hedetniemi
exaly +3 more sources
On the Global Roman Domination Number in Graphs
Iranian Journal of Science and Technology, Transactions A: Science, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source