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Discrete mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 19, pp. 5820 - 5827
... − X is adjacent to a vertex v ∈ X such that ( X − { v } ) ∪ { u } is dominating. The minimum cardinality of such a set is called the secure domination number, denoted by γ s ( G... 
ER-critical graph | Protection of a graph | Edge-removal-critical graph | Secure domination | MATHEMATICS | ROMAN-EMPIRE | TREES | PROTECTION
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 07/2014, Volume 171, pp. 15 - 27
...} is again a dominating set of G. The secure domination number of G, denoted by γs(G), is the cardinality of a smallest secure dominating set of G... 
Graph protection | Tree | Linear algorithm | Secure domination | (Wounded) spider | MATHEMATICS, APPLIED | GRAPHS | Algorithms | Trees | Spiders | Mathematical analysis | Pruning | Strategy | Graphs | Neighbouring
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2018, Volume 38, Issue 2, pp. 385 - 396
... ( { }) ∪ { } is a dominating set of . The secure domination problem is to determine a minimum secure dominating set... 
doubly chordal graph | secure domination | NP-complete | APX-complete | star convex bipartite graph | 05C69 | Doubly chordal graph | Secure domination | Star convex bipartite graph | MATHEMATICS | TREES | APPROXIMATION | HARDNESS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2019, Volume 262, pp. 179 - 184
.... The secure domination number γs(G) is the cardinality of a smallest secure dominating set of G... 
Graph algorithm | Secure domination | Cograph | MATHEMATICS, APPLIED | ALGORITHM | Apexes | Graph theory | Algorithms
Journal Article
Journal of combinatorial optimization, ISSN 1382-6905, 07/2020, Volume 40, Issue 1, pp. 98 - 109
.... The secure domination number of G, is the minimum cardinality of a secure dominating set in G. In the current era, security is definitely a desirable property for the interconnection networks and hence these type of study has wide applications. In this paper, we have studied the security number and secure domination number of Honeycomb Networks. 
Domination | Honeycomb networks | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Secure domination
Journal Article
Information processing letters, ISSN 0020-0190, 10/2015, Volume 115, Issue 10, pp. 786 - 790
...∖S is adjacent to a vertex v∈S such that (S∖{v})∪{u} is a dominating set. The secure domination number γs(G... 
Domination | Combinatorial problems | Computational complexity | Secure domination | Independence | TREES | COMPUTER SCIENCE, INFORMATION SYSTEMS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2018, Volume 247, pp. 70 - 76
.... The secure domination number γs(G) is the cardinality of a smallest secure dominating set of G... 
Domination | Linear time algorithm | Powers of a path | Proper interval graphs | Secure domination | MATHEMATICS, APPLIED | TREES | ALGORITHMS
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 06/2008, Volume 31, Issue 2, pp. 163 - 171
... ∈ S such that uv ∈ E and (S \ {v}) ∪ {u} is a dominating set of G. The minimum cardinality of a secure dominating set in G is the secure domination number γ s (G) of G... 
SECURE DOMINATION | VERTEX COVERS | Vertex covers | Secure domination | MATHEMATICS | vertex covers | secure domination | TREES
Journal Article
Information processing letters, ISSN 0020-0190, 05/2019, Volume 145, pp. 30 - 38
•We study the secure domination problem in cographs.•The secure domination problem is NP-hard for circle graphs.•An O(n+m... 
Domination | Cographs | Polynomial time algorithm | Graph algorithms | Secure domination | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS
Journal Article
Information processing letters, ISSN 0020-0190, 2017, Volume 119, pp. 14 - 18
•We give a characterization of trees with equal independent domination and secure domination numbers, which answers a question proposed by Merouane and Chellali (2015... 
Tree | Combinatorial problems | Secure domination number | Independent domination number | COMPUTER SCIENCE, INFORMATION SYSTEMS | GRAPHS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2014, Volume 178, pp. 27 - 32
.... We show that for all graphs, the weak Roman domination number is bounded above by the 2-rainbow domination number... 
Roman domination | Total domination | Weak Roman domination | 2-domination | Secure domination | 2-rainbow domination | MATHEMATICS, APPLIED | RAINBOW DOMINATION | GRAPHS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2019, Volume 260, pp. 289 - 293
In [Secure domination in proper interval graphs, Discrete Applied Mathematics 247 (2018) 70–76... 
Domination | Secure domination | Proper interval graphs | MATHEMATICS, APPLIED | Algorithms | Information management | Graphs | Applications of mathematics
Journal Article
Symmetry (Basel), ISSN 2073-8994, 2019, Volume 11, Issue 6, p. 831
.... The weight of a function f is defined to be w ( f ) = ∑ v ∈ V f ( v ) . In this article, we introduce the study of the total weak Roman domination number of a graph G, denoted by γ t r ( G... 
total Roman domination | NP-hard problem | secure total domination | PROTECTION | MULTIDISCIPLINARY SCIENCES | weak Roman domination | SECURE DOMINATION | total domination
Journal Article
International journal of applied engineering research, ISSN 0973-4562, 2019, Volume 14, Issue 7, pp. 1635 - 1637
Journal Article
Discrete mathematics, algorithms, and applications, ISSN 1793-8309, 12/2018, Volume 10, Issue 6
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 02/2018, Volume 236, pp. 23 - 29
A subset S of vertices in a graph G is a secure dominating set of G if S is a dominating set of G and, for each vertex u⁄∈S, there is a vertex v∈S such that uv... 
Lower bound | Maximal outerplanar graphs | Upper bound | Secure domination | MATHEMATICS, APPLIED | SETS
Journal Article
Open Journal of Mathematical Sciences, ISSN 2616-4906, 12/2018, Volume 2, Issue 1, pp. 134 - 145
For any graph \(G=(V,E)\), lict graph \(\eta(G)\) of a graph \(G\) is the graph whose vertex set is the union of the set of edges and the set of cut-vertices... 
Domination number; Lict graph; Secure domination; Secure lict domination
Journal Article
MATHEMATICS, ISSN 2227-7390, 04/2020, Volume 8, Issue 4, p. 600
In this article, we obtain general bounds and closed formulas for the secure total domination number of rooted product graphs... 
MATHEMATICS | domination | secure total domination | PROTECTION | ROMAN | rooted product graph | total domination
Journal Article
Journal of Combinatorial Optimization, ISSN 1382-6905, 2/2018, Volume 35, Issue 2, pp. 613 - 631
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 01/2017, Volume 40, Issue 1, pp. 1 - 12
...} is again a dominating set of G. The secure domination number of G, denoted by γs(G), is the cardinality... 
secure domination number | secure dominating set | Tree | MATHEMATICS | 05C69 | GRAPHS
Journal Article
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