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- 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 γ t-critical. If such a graph G has total domination number k, we call it k-γ t-critical. We characterize the… (More)

- 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 γ rk (G), which is the minimum sum of numbers of… (More)

- 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
- Graphs and Combinatorics
- 2015

- Teresa W. Haynes, Michael A. Henning, Lora Hopkins
- Discrete Mathematics
- 2004

- Michael A. Henning, Anders Yeo
- Graphs and Combinatorics
- 2007

In this paper we study tight lower bounds on the size of a maximum matching in a regular graph. For k ≥ 3, let G be a connected k-regular graph of order n and let α (G) be the size of a maximum matching in G. We show that if k is even, then α (G) ≥ min k 2 +4 k 2 +k+2 × n 2 , n−1 2 , while if k is odd, then α (G) ≥ (k 3 −k 2 −2) n−2k+2 2(k 3 −3k). We show… (More)

- Michael A. Henning
- Ars Comb.
- 2004

- Hossein Abdollahzadeh Ahangar, Michael A. Henning, Christian Löwenstein, Yancai Zhao, Vladimir Samodivkin
- J. Comb. Optim.
- 2014

- Robert C. Brigham, Teresa W. Haynes, Michael A. Henning, Douglas F. Rall
- Discrete Mathematics
- 2005