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- LUZ M. DEALBA, IRVIN R. HENTZEL, OLGA PRYPOROVA, BRYAN SHADER, KEVIN N. VANDER MEULEN
- 2006

A sign pattern Z (a matrix whose entries are elements of {+, −, 0}) is spectrally arbitrary if for any self-conjugate spectrum there is a real matrix with sign pattern Z having the given spectrum. Spectrally arbitrary sign patterns were introduced in [5], where it was (incorrectly) stated that if a sign pattern Z is reducible and each of its irreducible… (More)

We introduce some n-by-n sign patterns which allow for arbitrary spectrum and hence also arbitrary inertia. Consequently, we demonstrate that some known inertially arbitrary patterns are in fact spectrally arbitrary. We demonstrate that all inertially arbitrary patterns of order 3 are spectrally arbitrary and classify all spectrally arbitrary patterns of… (More)

A sign pattern is a matrix with entries in {+, −, 0}. A full sign pattern has no zero entries. The refined inertia of a matrix pattern is defined and techniques are developed for constructing potentially nilpotent full sign patterns. Such patterns are spectrally arbitrary. These techniques can also be used to construct potentially nilpotent sign patterns… (More)

- David A. Gregory, Brenda Heyink, Kevin N. Vander Meulen
- J. Comb. Theory, Ser. B
- 2003

We characterize the inertia of A + B for Hermitian matrices A and B when the rank of B is one. We use this to characterize the inertia of a partial join of two graphs. We then provide graph joins G for which the minimum number of complete bipartite graphs needed in a partition of the edge multi-set of G is equal to the maximum of the number of positive and… (More)

- Randall J. Elzinga, David A. Gregory, Kevin N. Vander Meulen
- Electronic Notes in Discrete Mathematics
- 2002

In a 1971 paper motivated by a problem on message routing in a communications network, Graham and Pollack propose a scheme for addressing the vertices of a graph G by N-tuples of three symbols in such a way that distances between vertices may readily be determined from their addresses. They observe that N h(D), the maximum of the number of positive and the… (More)

- Francesco Barioli, Wayne Barrett, +15 authors Amy Wangsness Wehe
- 2017

The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. This paper introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of vertices and uses it to bound the minimum rank… (More)

- Michael S. Cavers, In-Jae Kim, +4 authors KEVIN N. VANDER MEULEN
- 2005

A new family of minimal spectrally arbitrary patterns is presented which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [J. The novel approach here is the use of the Intermediate Value Theorem to avoid finding an explicit nilpotent realization of the new minimal spectrally arbitrary patterns. 1. Introduction. A matrix S… (More)

- David A. Gregory, Kevin N. Vander Meulen
- Journal of Graph Theory
- 1996

If G is a graph on n vertices and r 2 2, w e let m,(G) denote the minimum number of complete multipartite subgraphs, with r or fewer parts, needed to partition the edge set, f(G). In determining m,(G), w e may assume that no two vertices of G have the same neighbor set. For such reduced graphs G, w e prove that m,(G) 2 log,(n + r-l)/r. Furthermore, for each… (More)

- Jonathan Earl, Kevin N. Vander Meulen, Adam Van Tuyl
- Experimental Mathematics
- 2016

- Luz M. DeAlba, Irvin R. Hentzel, +9 authors KEVIN N. VANDER MEULEN
- 2017

A sign pattern Z (a matrix whose entries are elements of {+, −, 0}) is spectrally arbitrary if for any self-conjugate spectrum there is a real matrix with sign pattern Z having the given spectrum. Spectrally arbitrary sign patterns were introduced in [5], where it was (incorrectly) stated that if a sign pattern Z is reducible and each of its irreducible… (More)