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mathematics (46) 46
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domination (15) 15
discrete mathematics and combinatorics (12) 12
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The Australasian journal of combinatorics, ISSN 1034-4942, 2017, Volume 69, Issue 2, pp. 243 - 258
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2015, Volume 35, Issue 2, pp. 283 - 300
Eternal and m-eternal domination are concerned with using mobile guards to protect a graph against infinite sequences of attacks at vertices. Eternal... 
eternal dominating set | clique cover | dominating set | independent set | Independent set | Eternal dominating set | Dominating set | Clique cover | MATHEMATICS | GRAPHS
Journal Article
Discrete mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 20, pp. 5950 - 5962
A broadcast on a graph G is a function f : V → { 0 , … , diam G } such that for each v ∈ V , f ( v ) ≤ e ( v ) (the eccentricity of v ). The broadcast number... 
Radial tree | Dominating broadcast | Broadcast | Broadcast domination | MATHEMATICS
Journal Article
Discrete mathematics, ISSN 0012-365X, 2009, Volume 309, Issue 19, pp. 5820 - 5827
A secure dominating set X of a graph G is a dominating set with the property that each vertex u ∈ V G − X is adjacent to a vertex v ∈ X such that ( X − { v } )... 
ER-critical graph | Protection of a graph | Edge-removal-critical graph | Secure domination | MATHEMATICS | ROMAN-EMPIRE | TREES | PROTECTION
Journal Article
Discrete mathematics, ISSN 0012-365X, 2019, Volume 342, Issue 1, pp. 145 - 151
Journal Article
Journal of Combinatorial Mathematics and Combinatorial Computing, ISSN 0835-3026, 02/2018, Volume 104, pp. 217 - 230
Journal Article
Discrete mathematics, ISSN 0012-365X, 2006, Volume 306, Issue 21, pp. 2647 - 2654
We provide a simple constructive characterization for trees with equal domination and independent domination numbers, and for trees with equal domination and... 
Domination | Trees | Equality | Independence | PERFECT GRAPHS | MATHEMATICS | domination | NUMBERS | IRREDUNDANCE | independence | trees | equality
Journal Article
Journal of Combinatorial Mathematics and Combinatorial Computing, ISSN 0835-3026, 05/2015, Volume 93, pp. 131 - 152
Journal Article
Discrete mathematics, ISSN 0012-365X, 01/2019, Volume 342, Issue 1, pp. 145 - 151
For a graph G=(V,E), the k-dominating graph Dk(G) of G has vertices corresponding to the dominating sets of G having cardinality at most k, where two vertices... 
[formula omitted]-dominating graph | Domination reconfiguration problem | k-dominating graph | MATHEMATICS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 03/2017, Volume 220, pp. 80 - 90
A broadcast on a nontrivial connected graph G=(V,E) is a function f:V→{0,1,…,diam(G)} such that f(v)≤e(v) (the eccentricity of v) for all v∈V. The cost of f is... 
Broadcast irredundance | Broadcast domination | MATHEMATICS, APPLIED | INDEPENDENCE | Mathematics - Combinatorics
Journal Article
The Australasian journal of combinatorics, ISSN 1034-4942, 2013, Volume 56, pp. 3 - 22
Journal Article
The Australasian journal of combinatorics, ISSN 1034-4942, 2014, Volume 58, Issue 2, pp. 249 - 263
Journal Article
The Australasian journal of combinatorics, ISSN 1034-4942, 2015, Volume 61, Issue 3, pp. 251 - 272
Journal Article
The Australasian journal of combinatorics, ISSN 1034-4942, 2008, Volume 40, pp. 279 - 291
Journal Article
01/2017, ISBN 1351454641
Book Chapter
01/2017, ISBN 1351454641
Book Chapter
Applicable analysis and discrete mathematics, ISSN 1452-8630, 4/2016, Volume 10, Issue 1, pp. 1 - 29
Mobile guards on the vertices of a graph are used to defend it against attacks on either its vertices or its edges. Various models for this problem have been... 
Integers | Network servers | Algorithms | Cardinality | Military defense | Induced subgraphs | Games | Military strategy | Vertices | Graph protection | Eternal dominating set | Dominating set | Eternal vertex cover | MATHEMATICS | MATHEMATICS, APPLIED | ROMAN-EMPIRE | GRID GRAPHS | STRATEGY | Graph Protection | Eternal Vertex Cover | Eternal Dominating Set | ETERNAL DOMINATION | SERVER PROBLEMS
Journal Article
Discrete mathematics, ISSN 0012-365X, 06/2013, Volume 313, Issue 11, pp. 1224 - 1232
An edge ordering of a graph G is an injection f:E→R, the set of real numbers. A path in G for which the edge ordering f increases along its edge sequence is... 
Edge ordering of a graph | Depression | Increasing path | Monotone path | MATHEMATICS | MONOTONE PATHS | Depression, Mental
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2012, Volume 160, Issue 7-8, pp. 1183 - 1190
The eternal domination problem requires a graph to be protected against an infinitely long sequence of attacks on vertices by guards located at vertices, the... 
Vertex cover | Eternal dominating set | MATHEMATICS, APPLIED | GRAPHS | Guards | Mathematical analysis | Graphs
Journal Article
Discrete mathematics, ISSN 0012-365X, 11/2014, Volume 335, pp. 100 - 109
Mobile guards on the vertices in an independent set X of a graph G are used to defend G against an infinite sequence of attacks on up to k independent vertices... 
Graph protection | Eternal domination | Independent protection | Multicolouring independent domination | [formula omitted]-protecting set | i -protecting set | MATHEMATICS | i-protecting set
Journal Article
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