Note on Nordhaus-Gaddum Problems for Colin de Verdière type Parameters

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2013-10-07
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Barrett, Wayne
Fallat, Shaun
Hall, H. Tracy
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Hogben, Leslie
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Electrical and Computer Engineering

The Department of Electrical and Computer Engineering (ECpE) contains two focuses. The focus on Electrical Engineering teaches students in the fields of control systems, electromagnetics and non-destructive evaluation, microelectronics, electric power & energy systems, and the like. The Computer Engineering focus teaches in the fields of software systems, embedded systems, networking, information security, computer architecture, etc.

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The Department of Electrical Engineering was formed in 1909 from the division of the Department of Physics and Electrical Engineering. In 1985 its name changed to Department of Electrical Engineering and Computer Engineering. In 1995 it became the Department of Electrical and Computer Engineering.

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1909-present

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  • Department of Electrical Engineering (1909-1985)
  • Department of Electrical Engineering and Computer Engineering (1985-1995)

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Mathematics
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We establish the bounds 4 3 6 b 6 b 6 p 2, where b and b are the Nordhaus-Gaddum sum upper bound multipliers, i.e., (G)+(G) 6 bjGj and (G)+(G) 6 bjGj for all graphs G, and and are Colin de Verdiere type graph parameters. The Nordhaus-Gaddum sum lower bound for and is conjectured to be jGj 2, and if these parameters are replaced by the maximum nullity M(G), this bound is called the Graph Complement Conjecture in the study of minimum rank/maximum nullity problems.

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This article is published as Barrett, Wayne, Shaun M. Fallat, H. Tracy Hall, and Leslie Hogben. "Note on Nordhaus-Gaddum Problems for Colin de Verdière type Parameters." The Electronic Journal of Combinatorics 20, no. 3 (2013): P56. DOI: 10.37236/2570. Posted with permission.

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Tue Jan 01 00:00:00 UTC 2013
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