On the Distance Spectra of Graphs
Date
Authors
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Research Projects
Organizational Units
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.
History
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.
Dates of Existence
1909-present
Historical Names
- Department of Electrical Engineering (1909-1985)
- Department of Electrical Engineering and Computer Engineering (1985-1995)
Related Units
- College of Engineering (parent college)
- Department of Physics and Electrical Engineering (predecessor)
Journal Issue
Is Version Of
Versions
Series
Department
Abstract
The distance matrix of a graph G is the matrix containing the pairwise distances between vertices. The distance eigenvalues of G are the eigenvalues of its distance matrix and they form the distance spectrum of G. We determine the distance spectra of double odd graphs and Doob graphs, completing the determination of distance spectra of distance regular graphs having exactly one positive distance eigenvalue. We characterize strongly regular graphs having more positive than negative distance eigenvalues. We give examples of graphs with few distinct distance eigenvalues but lacking regularity properties. We also determine the determinant and inertia of the distance matrices of lollipop and barbell graphs.
Comments
This is a manuscript of an article published as Aalipour, Ghodratollah, Aida Abiad, Zhanar Berikkyzy, Jay Cummings, Jessica De Silva, Wei Gao, Kristin Heysse et al. "On the distance spectra of graphs." Linear Algebra and its Applications 497 (2016): 66-87. DOI: 10.1016/j.laa.2016.02.018. Posted with permission.