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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, 05/2013, Volume 313, Issue 10, pp. 1087 - 1097
The domination number γ(G) of a graph G is the least number of vertices in a dominating set of G, and the lower irredundance number ir(G) is the least number... 
Vertex-critical | Domination | Irredundance | Coalescence | MATHEMATICS
Journal Article
Utilitas Mathematica, ISSN 0315-3681, 11/2004, Volume 66, pp. 137 - 163
The notion of a graph theoretic Ramsey number is generalised by assuming that both the original graph whose edges are arbitrarily bi-coloured and the sought... 
Multipartite/circulant graph | Set/size multipartite ramsey number | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | IRREDUNDANT | set/size multipartite Ramsey number | S(3,7) | multipartite/circulant graph
Journal Article
Utilitas Mathematica, ISSN 0315-3681, 05/2005, Volume 67, pp. 19 - 32
For vertex v of a simple n-vertex graph G = (V, E) let f (v) be the number of guards stationed at v. A guard at v can deal with a problem at any vertex in its... 
MATHEMATICS, APPLIED | STATISTICS & PROBABILITY
Journal Article
Utilitas Mathematica, ISSN 0315-3681, 11/2006, Volume 71, pp. 161 - 168
The notion of higher order domination in graphs has been studied in the literature and may be categorised as so-called finite higher order domination and... 
Higher order domination | Multipartite graph | Weak roman domination | Protection | Secure domination | MATHEMATICS, APPLIED | secure domination | multipartite graph | weak Roman domination | STATISTICS & PROBABILITY | protection | higher order domination
Journal Article
Utilitas Mathematica, ISSN 0315-3681, 03/2006, Volume 69, pp. 143 - 160
The notions of the flatness of an edge-ordering and of the depression of a simple graph are introduced. Some general properties of these parameters are... 
Edge-ordering | Depression | Height | Ascent | Altitude | Flatness | altitude | MATHEMATICS, APPLIED | ascent | flatness | edge-ordering | MONOTONE PATHS | STATISTICS & PROBABILITY | depression | height
Journal Article
Utilitas Mathematica, ISSN 0315-3681, 07/2008, Volume 76, pp. 65 - 77
The Delta(d)-chromatic number of a graph G, denoted by chi(Delta)(d)(G), is the smallest number of colours with which the vertices of G may be coloured so that... 
Defective/maximum degree graph colouring | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | maximum degree graph colouring | defective
Journal Article
Discrete mathematics, ISSN 0012-365X, 2001, Volume 231, Issue 1, pp. 221 - 239
For π any of the basic domination parameters ir, γ, i, β, Γ or IR, we study graphs for which π increases whenever an edge is removed ( π-ER-critical graphs)... 
Domination | Irredundance | Edge-removal-critical graph | Independence | MATHEMATICS | irredundance | domination | edge-removal-critical graph | independence
Journal Article
Discrete mathematics, ISSN 0012-365X, 2003, Volume 266, Issue 1, pp. 185 - 193
Denote the upper irredundance number of a graph G by IR( G). A graph G is IR-edge-addition-sensitive if its upper irredundance number changes whenever an edge... 
Irredundance | Upper irredundance critical graph | Upper irredundance number | MATHEMATICS | upper irredundance number | DOMINATION | irredundance | upper irredundance critical graph
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 08/2001, Volume 37, Issue 4, pp. 205 - 212
Let π be any of the domination parameters ir γ, i, β, Γ or IR. The graph G is π‐critical (π+‐critical) if the removal of any vertex of G causes π(G) to... 
criticality | irredundance | domination | Domination | Irredundance | Criticality | MATHEMATICS | dominations
Journal Article
Ars combinatoria, ISSN 0381-7032, 2001, Volume 59, pp. 279 - 288
Let H-1, ..., H-t be classes of graphs. The class Ramsey number R(H-1 ,...,H-t) is the smallest integer n such that for each t-edge colouring (G(1), ..., G(t))... 
MATHEMATICS
Journal Article
Discrete mathematics, ISSN 0012-365X, 2001, Volume 231, Issue 1, pp. 123 - 134
For each vertex s of the subset S of vertices of a graph G, we define Boolean variables p, q, r which measure the existence of three kinds of S-private... 
Irredundance | Generalised irredundance | Generalised Ramsey theory | MATHEMATICS | generalised Ramsey theory | irredundance | generalised irredundance
Journal Article
Quaestiones Mathematicae, ISSN 1607-3606, 04/1996, Volume 19, Issue 1-2, pp. 291 - 313
A 0-dominating function 0DF of a graph G = (V,E) is a function f: V → [0,1] such that Σ xεN(v) f(x) ≥ 1 for each ν ε V with f(v) = 0. The aggregate of a 0DF f... 
Journal Article
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