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- Craig E. Larson, Ryan Pepper
- Electr. J. Comb.
- 2011

The annihilation number a of a graph is an upper bound of the independence number Î± of a graph. In this article we characterize graphs with equal independence and annihilation numbers. In particular,â€¦ (More)

- Craig E. Larson, Nicolas Van Cleemput
- Artif. Intell.
- 2016

We discuss a new implementation of, and new experiments with, Fajtlowiczâ€™s Dalmatian conjecture-making heuristic. Our program makes conjectures about relations of real number invariants ofâ€¦ (More)

- Craig E. Larson
- Eur. J. Comb.
- 2011

An independent set Ic is a critical independent set if |Ic|âˆ’|N(Ic)| â‰¥ |J | âˆ’ |N(J)|, for any independent set J . The critical independence number of a graph is the cardinality of a maximum criticalâ€¦ (More)

The total domination number Î³t(G) of a simple, undirected graph G is the order of a smallest subset D of the vertices of G such that each vertex of G is adjacent to some vertex in D. In this paper weâ€¦ (More)

The k-domination number Î³k(G) of a simple, undirected graph G is the order of a smallest subset D of the vertices of G such that each vertex of G is either in D or adjacent to at least k vertices inâ€¦ (More)

- Ghidewon Abay-Asmerom, Richard Hammack, Craig E. Larson, Dewey T. Taylor
- SIAM J. Discrete Math.
- 2010

Given a connected bipartite graph G, we describe a procedure which enumerates and computes all graphs H (if any) for which there is a direct product factorization G âˆ¼= H Ã— K2. We apply this techniqueâ€¦ (More)

- Ermelinda DeLaViÃ±a, Craig E. Larson, Ryan Pepper, Bill Waller
- Graphs and Combinatorics
- 2012

In a classical 1986 paper by ErdÃ¶s, Saks and SÃ³s every graph of radius r has an induced path of order at least 2r âˆ’ 1. This result implies that the independence number of such graphs is at least r .â€¦ (More)

- Craig E. Larson, Nicolas Van Cleemput
- Annals of Mathematics and Artificial Intelligence
- 2017

Discovery in mathematics is a prototypical intelligent behavior, and an early and continuing goal of artificial intelligence research. We present a heuristic for producing mathematical conjectures ofâ€¦ (More)

An independent set Ic is a critical independent set if |Ic| âˆ’ |N(Ic)| â‰¥ |J | âˆ’ |N(J)|, for any independent set J . The critical independence number of a graph is the cardinality of a maximum criticalâ€¦ (More)

The total domination number of a simple, undirected graph G is the minimum cardinality of a subset D of the vertices of G such that each vertex of G is adjacent to some vertex in D. In 2007â€¦ (More)