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- Teresa W. Haynes, Sandra Mitchell Hedetniemi, Stephen T. Hedetniemi, Michael A. Henning
- SIAM J. Discrete Math.
- 2002

Assume we have a set of k colors and to each vertex of a graph G we assign an arbitrary subset of these colors. If we require that each vertex to which an empty set is assigned has in its neighborhood all k colors, then this is called the k-rainbow dominating function of a graph G. The corresponding invariant γrk(G), which is the minimum sum of numbers of… (More)

- Wayne Goddard, Teresa W. Haynes, Michael A. Henning, Lucas C. van der Merwe
- Discrete Mathematics
- 2004

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G− v is less than the total domination number of G. These graphs we call γt-critical. If such a graph G has total domination number k, we call it k-γt-critical. We characterize the… (More)

- Michael A. Henning
- Discrete Mathematics
- 2004

- Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning
- Electr. J. Comb.
- 2003

A defensive alliance in a graph G = (V,E) is a set of vertices S ⊆ V satisfying the condition that for every vertex v ∈ S, the number of neighbors v has in S plus one (counting v) is at least as large as the number of neighbors it has in V − S. Because of such an alliance, the vertices in S, agreeing to mutually support each other, have the strength of… (More)

- Michael A. Henning
- Discrete Mathematics
- 2009

A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. In this paper, we offer a survey of selected recent results on total domination in graphs. c © 2008 Elsevier B.V. All rights reserved.

- Michael Dorfling, Michael A. Henning
- Discrete Applied Mathematics
- 2006

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems in graphs (see [T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, M.A. Henning, Power domination in graphs applied to electrical power networks, SIAM J. Discrete… (More)

- Bostjan Bresar, Michael A. Henning, Douglas F. Rall
- Electronic Notes in Discrete Mathematics
- 2005

- Johannes H. Hattingh, Michael A. Henning
- Discrete Mathematics
- 1998

- Michael A. Henning
- Ars Comb.
- 2006