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

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

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

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

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

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

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

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

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

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

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

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

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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