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HPIEPER-Spectral-Inequalities.pdf (464.83 KB)

ETD Abstract Container

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Comparing Two Thickened Cycles: A Generalization of Spectral Inequalities

Pieper, Hannah E
http://orcid.org/0000-0001-6728-3250
http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528367417905844

Abstract Details

2018, BA, Oberlin College, Mathematics.
Motivated by an effort to simplify the Watts-Strogatz model for small-world networks, we generalize a theorem concerning interlacing inequalities for the eigenvalues of the normalized Laplacians of two graphs differing by a single edge. Our generalization allows weighted edges and certain instances of self loops. These inequalities were first proved by Chen et. al in [2] but our argument generalizes the simplified argument given by Li in [8].
Elizabeth L. Wilmer (Advisor)
28 p.
Mathematics
spectral graph theory; eigenvalues; interlacing inequalities

Recommended Citations

Citations

  • Pieper, H. E. (2018). Comparing Two Thickened Cycles: A Generalization of Spectral Inequalities [Undergraduate thesis, Oberlin College]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528367417905844

    APA Style (7th edition)

  • Pieper, Hannah. Comparing Two Thickened Cycles: A Generalization of Spectral Inequalities . 2018. Oberlin College, Undergraduate thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528367417905844.

    MLA Style (8th edition)

  • Pieper, Hannah. "Comparing Two Thickened Cycles: A Generalization of Spectral Inequalities ." Undergraduate thesis, Oberlin College, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528367417905844

    Chicago Manual of Style (17th edition)

oberlin1528367417905844
239
© 2018, all rights reserved.
This open access ETD is published by Oberlin College Honors Theses and OhioLINK.