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Applicable analysis and discrete mathematics, ISSN 1452-8630, 10/2016, Volume 10, Issue 2, pp. 501 - 517
A Roman dominating function on a graph 𝐺 is a function 𝑓: 𝑉 (𝐺) → {0, 1, 2} satisfying the condition that every vertex 𝑢 for which 𝑓(𝑢) = 0 is adjacent... 
Leaves | Literature | Mathematical theorems | Cardinality | Double stars | Discrete mathematics | Mathematical functions | Graph theory | Mathematical minima | Vertices | Roman domination | Total Roman domination | Total domination | Domina-tion | Domination | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
07/2020
In this paper we begin an exploration of several domination-related parameters (among which are the total, restrained, total restrained, paired, outer... 
Mathematics - Combinatorics
Journal Article
Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 2, pp. 293 - 303
A dominating set of a graph 𝐺 which intersects every independent set of maximum cardinality in 𝐺 is called an independent transversal dominating set. The... 
Integers | Cardinality | Mathematical sets | Polynomials | Graph theory | Vertices | Realizability | Domination | Transversal | Independent transversal domination | Independence | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | MAXIMUM STABLE SETS
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 2/2014, Volume 27, Issue 2, pp. 241 - 255
... Löwenstein · Yancai Zhao · Vladimir Samodivkin Published online: 22 June 2012 © Springer Science+Business Media, LLC 2012 Abstract In this paper we continue the study... 
Convex and Discrete Geometry | Operations Research/Decision Theory | Signed domination | Roman domination | Signed Roman domination | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Optimization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Journal Article
The Australasian journal of combinatorics, ISSN 1034-4942, 2018, Volume 71, Issue 2, pp. 303 - 311
Journal Article
Communications in combinatorics and optimization, ISSN 2538-2128, 01/2018, Volume 3, Issue 1, pp. 1 - 24
A Roman dominating function (RDF) on a graph $G = (V‎, ‎E)$‎ ‎is a labeling $f‎ : ‎V \rightarrow \{0‎, ‎1‎, ‎2\}$ such‎ ‎that every vertex with label $0$ has a... 
Roman domination number | coalescence | excellent tree
Journal Article
Indian Journal of Mathematics, ISSN 0019-5324, 08/2018, Volume 60, Issue 2, pp. 287 - 300
Journal Article
Discussiones Mathematicae. Graph Theory, ISSN 1234-3099, 2018
Journal Article
Mathematica bohemica, ISSN 0862-7959, 2017, Volume 142, Issue 1, pp. 9 - 20
For a graphical property $\mathcal{P}$ and a graph $G$, a subset $S$ of vertices of $G$ is a $\mathcal{P}$-set if the subgraph induced by $S$ has the property... 
Domination multisubdivision number | Dominating set | Hereditary graph property | Edge subdivision | domination multisubdivision number | edge subdivision | dominating set | hereditary graph property
Journal Article
IEEE access, ISSN 2169-3536, 2019, Volume 7, pp. 72604 - 72612
Domination number is of practical interest in several theoretical and applied scenes. In the problem of wireless networking, the dominating idea is used to... 
2-rainbow independent domination number | 2-rainbow independent domination stable graph | Computer architecture | tree | Mathematics | Ad hoc networks | Internet | Security | Civil engineering | STEM | NUMBER | PETERSEN GRAPHS P(N | PRODUCT | COMPUTER SCIENCE, INFORMATION SYSTEMS | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
01/2018
Given a graph $G = (V,E)$ and two its distinct vertices $u$ and $v$. The $(u,v)$-$P_k$-{\em addition graph} of $G$ is the graph $G_{u,v,k-2}$ obtained from... 
Mathematics - Combinatorics
Journal Article
AKCE International Journal of Graphs and Combinatorics, ISSN 0972-8600, 08/2016, Volume 13, Issue 2, pp. 140 - 145
In this paper we give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph... 
(Total) restrained/Roman bondage number | Total/(weakly) connected domination number | Orientable/nonorientable genus | Euler characteristic
Journal Article
09/2017
A Roman dominating function (RD-function) on a graph $G = (V(G), E(G))$ is a labeling $f : V(G) \rightarrow \{0, 1, 2\}$ such that every vertex with label $0$... 
Mathematics - Combinatorics
Journal Article
Transactions on combinatorics, ISSN 2251-8657, 09/2017, Volume 6, Issue 3, pp. 1 - 9
‎Let $delta (G)$‎, ‎$Delta (G)$ and $gamma(G)$‎ ‎be the minimum degree‎, ‎maximum degree and‎ ‎domination number of a graph $G=(V(G)‎, ‎E(G))$‎,... 
domination/domatic/idomatic number | efficient dominating set
Journal Article
Electronic journal of graph theory and applications, ISSN 2338-2287, 2018, Volume 6, Issue 1, pp. 1 - 16
The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number. We obtain... 
Bondage number | Euler's formula | Average degree | Girth | Domination number | bondage number, domination number, euler's formula, girth, average degree
Journal Article
The Australasian journal of combinatorics, ISSN 1034-4942, 08/2015, Volume 63, Issue 1, pp. 41 - 57
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 10/2007, Volume 57, Issue 5, pp. 401 - 406
The k-restricted domination number of a graph G is the minimum number d k such that for any subset U of k vertices of G, there is a dominating set in G... 
Mathematics, general | Mathematics | Algebra | Primary 05C69 | dominating set | restricted domination number | MATHEMATICS | NUMBER | MINIMUM DEGREE-2
Journal Article
10/2016
A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V \rightarrow \{0, 1, 2\}$ such that every vertex with label $0$ has a neighbor... 
Mathematics - Combinatorics
Journal Article
01/2016
For a graph $G$ let $\gamma (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient domination graph (or a hypo-$\mathcal{ED}$ graph) if... 
Mathematics - Combinatorics
Journal Article
08/2015
For a graph $G = (V, E)$, a Roman dominating function $f : V \rightarrow \{0, 1, 2\}$ has the property that every vertex $v \in V $with $f (v) = 0$ has a... 
Mathematics - Combinatorics
Journal Article
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