J. Hattingh

Publications
Influence

On weakly connected domination in graphs

J. Dunbar, J. Grossman, J. Hattingh, S. Hedetniemi, Alice A. McRae
Computer Science, Mathematics
Discret. Math.
15 April 1997

A dominating set D is a weakly connected dominating set of a connected graph G if (V,E@?(DxV)) is connected. Expand

The algorithmic complexity of signed domination in graphs

J. Hattingh, M. Henning, P. Slater
Mathematics, Computer Science
Australas. J Comb.
1995

A two-valued function f defined on the vertices of a graph G (V, E), I : V -+ {-I, I}, is a signed dominating function if the sum of its function values over any closed neighborhood is at least one. Expand

Majority domination in graphs

I. Broere, J. Hattingh, M. Henning, Alice A. McRae
Computer Science, Mathematics
Discret. Math.
6 March 1995

A two-valued function f defined on the vertices of a graph G = (V, E) is a majority dominating function if the sum of its function values over at least half the closed neighborhoods is at least one. Expand

Star-path bipartite Ramsey numbers,

J. Hattingh, M. Henning
Computer Science, Mathematics
Discret. Math.
1 April 1998

In this note, we establish the exact value of the bipartite Ramsey number b ( P m , K l , n ) for all integers m , n ⩾ 2, where P m denotes a path on m vertices. Expand

Restrained domination in graphs

Gayla S. Domke, J. Hattingh, S. Hedetniemi, R. Laskar, L. Markus
Computer Science, Mathematics
Discret. Math.
28 May 1999

A restrained dominating set is a set S ⊆ V where every vertex in V − S is adjacent to a vertex in S as well as another vertex inV . Expand

Restrained domination in trees

Gayla S. Domke, J. Hattingh, M. Henning, L. Markus
Computer Science, Mathematics
Discret. Math.
28 January 2000

We show that if T is a tree of order n , then γ r (T)⩾⌈(n+2)/3⌉ is the smallest cardinality of a restrained dominating set of G . Expand

PRODUCTS OF CIRCULANT GRAPHS

I. Broere, J. Hattingh
Mathematics
1990

ABSTRACT Graph products of circulants are studied. It is shown that if G and H are circulants and gcd(v(G), v(H)) = 1, then every B-product of G and H is again a circulant. We prove that if m ≠ 2,… Expand

Total restrained domination in unicyclic graphs 1

J. Hattingh, Ernst J. Joubert, E. Jonck, A. Plummer
2008

Let G = (V, E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex in V is adjacent to a vertex in S and every vertex of V −S is adjacent to a vertex in V −S. The total… Expand

The ratio of the distance irredundance and domination numbers of a graph

J. Hattingh, M. Henning
Mathematics
3 January 1994

Let n ≥ 1 be an integer and let G be a graph. A set D of vertices in G is defined to be an n-dominating set of G if every vertex of G is within distance n from some vertex of D. The minimum… Expand

Using maximality and minimality conditions to construct inequality chains

E. Cockayne, J. Hattingh, S. M. Hedetniemi, S. Hedetniemi, Alice A. McRae
Computer Science, Mathematics
Discret. Math.
15 November 1997

We define a simple mechanism which explains why this inequality chain exists and how it is possible to define many similar chains of potentially arbitrary length. Expand

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