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- Matthew Booth, Philip Hackney, +8 authors Wendy Wang
- SIAM J. Matrix Analysis Applications
- 2008

- Gerald Haynes, Catherine Park, Amanda Schaeffer, Jordan Webster, Lon H. Mitchell
- Electr. J. Comb.
- 2010

A vector coloring of a graph is an assignment of a vector to each vertex where the presence or absence of an edge between two vertices dictates the value of the inner product of the corresponding vectors. In this paper, we obtain results on orthogonal vector coloring, where adjacent vertices must be assigned orthogonal vectors. We introduce two vector… (More)

- Francesco Barioli, Shaun M. Fallat, +4 authors Sivaram K. Narayan
- 2017

Let G = (V, E) be a multigraph with no loops on the vertex set V = {1, 2, . . . , n}. Define S+(G) as the set of symmetric positive semidefinite matrices A = [aij ] with aij 6= 0, i 6= j, if ij ∈ E(G) is a single edge and aij = 0, i 6= j, if ij / ∈ E(G). Let M+(G) denote the maximum multiplicity of zero as an eigenvalue of A ∈ S+(G) and mr+(G) = |G|−M+(G)… (More)

The Colin de Verdière parameters, μ and ν, are defined to be the maximum nullity of certain real symmetric matrices associated with a given graph. In this work, both of these parameters are calculated for all chordal graphs. For ν the calculation is based solely on maximal cliques, while for μ the calculation depends on split subgraphs. For the case of μ… (More)

- Lon H. Mitchell
- Discrete Mathematics
- 2004

- Lon H. Mitchell
- Respiratory therapy
- 1982

The quality of services provided by respiratory therapists must be measured as part of a hospital's overall evaluation of patient care, as mandated by the Joint Commission on the Accreditation of Hospitals. An internal audit helps both the respiratory therapists and the attending physicians to know what kind of specific documentation is needed in the… (More)

- Jonathan E. Beagley, Lon H. Mitchell, +5 authors A. Matthew Zimmer
- 2013

Article history: Received 10 June 2011 Accepted 10 July 2012 Available online 11 october 2012 Submitted by W. Barrett

This paper is the result of undergraduate research done at Central Michigan University under the guidance of Dr. Sivaram K. Narayan, and was made possible in part by a grant from the Dean of the College of Science and Technology during the summer of 1998, and a CMU Summer Research Scholarship in the summer of 1999. I am very greatful to Dr. Narayan for his… (More)

The minimum vector rank (mvr) of a graph over a field F is the smallest d for which a faithful vector representation of G exists in Fd . For simple graphs, minimum semidefinite rank (msr) and minimum vector rank differ by exactly the number of isolated vertices. We explore the relationship between msr and mvr for multigraphs and show that a result linking… (More)

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