College of Natural & Social Sciences

Department of Mathematics

**Office**STF317

Phone

x3-2150

Email

**Teaching**

## Publications

- Mike Krebs, Maya Sankar. Abelian groups with 3-chromatic Cayley graphs. Preprint.
- A Graph Theorist Plants a Tree, The College Mathematics Journal (2024), joint work with Cal State LA students A. Carrillo, J. Cervantes, and F. Leon.
- A generalization of Zhu's theorem on six-valent integer distance graphs, joint work with Cal State LA student J. Cervantes. Preprint.
- Chromatic numbers of Cayley graphs of abelian groups: Cases of small dimension and rank, joint work with Cal State LA student J. Cervantes. Preprint.
- Authors' Notes for "Chromatic numbers of abelian Cayley graphs: A matrix method" (bonus content: a Mathematica file with code for computing the chromatic number of a standardized abelian Cayley graph associated to a 1 x r, m x 1, 2 2 x 2, or 3 x 2 matrix.)
- Chromatic numbers of Cayley graphs of abelian groups: A matrix method, joint work with Cal State LA student J. Cervantes. Linear Algebra and its Applications

Volume 676, 1 November 2023, pp. 277-295. (The arXiv version this links to corrects an error in an example that appears in the published version.) - Kazhdan constants and isomorphic graph pairs, joint work with Cal State LA students M. Davila, T. Hayes, M. Krebs, and M. Reyes. Algebra and Discrete Mathematics, Volume 35 (2023). Number 1, pp. 73-85.
- Clique numbers of finite unit-quadrance graphs, Journal of Algebraic Combinatorics, 57, 1-20 (2023)
- What Baseball Team Does PageRank Say Was The Best Ever?, Baseball Research Journal, Spring 2022. Joint work with Cal State LA student Gwen Ostergren
- Finite epsilon unit-distance graphs. Journal of Algebra, Combinatorics, Discrete Structures, and Applications, Sept. 2021; 8(3): 161-166
- Can a Subset's Topology Detect Continuous Extensions? The College Mathematics Journal, 49(2): 138-139, March 2018.
- On cardinalities and compact closures. Applied General Topology, 18(1): 107, April 2017, 107-115
- Kevin Cramer (CSULA student), Mike Krebs, Nicole Shabazi (CSULA student), Anthony Shaheen and Edward Voskanian (CSULA student). The Isoperimetric constant and Kazhdan constant of a Paley graph, Involve, 9(2): 293-306, March 2016.
- Al Fares, A. (CSULA student), E. Golvin (CSULA student), M. Krebs. A class of 2-groups of derived length three. Serdica Mathematical Journal, Volume 41, Numbers 2-3, 2015, pp. 329-332
- ZERO SUMS ON UNIT SQUARE VERTEX SETS, AND PLANE COLORINGS. Joint work with R. Katz and A. Shaheen. The American Mathematical Monthly. Vol. 121, No. 7 (August-September 2014), pp. 610-618
- Expander graphs. In J. Gross and J. Yellen (Eds.), Handbook of Graph Theory, Second Edition. CRC Press, 2013
- Expander families, group structure, and semidirect products. Joint work with M. Aivazian (CSULA student). Bulletin of the Irish Mathematical Society, Number 71 (2013), 21-30
- Simple examples of the combinatorial trace method in action. Joint work with N. Martinez (CSULA student). College Mathematics Journal, Vol. 44 (2013), no. 1, 32-36
- A combinatorial trace method: Counting closed paths to assay graph eigenvalues. Joint work with K. Dsouza (CSULA student). Rocky Mountain Journal of Mathematics, Vol. 43 (2013), no. 2, 469-478
- K-quasiderivations. (K-quasiderivations are maps that satisfy both the Product Rule and Chain Rule.) Central European Journal of Mathematics, Vol. 10 (2012), no. 2, 824-834
- Expander Families and Cayley Graphs: A Beginner's Guide, co-authored by A. Shaheen, Oxford University Press, New York, Oct. 2011
- mini-Sudokus and Groups. Joint work with C. Arcos (CSULA student) and G. Brookfield. Math. Mag. 83 (2010), no. 2, 111-122
- On Cantor's first uncountability proof, Pick's theorem, and the irrationality of the golden ratio. Joint work with T. Wright. Amer. Math. Monthly 117 (2010), no. 7, 633-637
- How to differentiate an integer modulo n. Joint work with C. Emmons and A. Shaheen. College Mathematics Journal, November 2009
- Faculty adviser for Fixed Points of Number Derivatives Modulo n by CSULA student F. Bains. Rose-Hulman Undergraduate Math Journal, Vol. 10 (2009), Issue 1
- Think Around The Box, a crossword puzzle of sorts. The Mathematical Intelligencer, Volume 31, Number 2, 59-60
- On the Spectra of Johnson Graphs. Joint work with A. Shaheen. (Appears in Electronic Journal of Linear Algebra, Volume 17, pp. 154-167, March 2008)
- Toledo invariants of Higgs bundles on elliptic surfaces associated to base orbifolds of Seifert fibered homology 3-spheres. (Appears in Michigan Math. J. Volume 56, Issue 1 (2008), 3-27.)
- My Ph.D. dissertation

## Master's theses supervised

- Standardized Abelian Cayley Graphs and Their Chromatic Numbers In Four Dimensions by Timothy Harris
- Kazhdan Constants for Finite Cyclic Groups by Travis Hayes
- Kazhdan Constants Associated with Isomorphic Cayley Graphs by Manuel Davila
- To what Extent is the Kazhdan Constant a Graph Invariant? by Marcos Reyes
- Semidirect product of the integers modulo two by Ahmed Al-Fares
- Lower bounds on the orders of the terms of the derived series of finite 2-groups of derived length 3 by Ezekiel Golvin
- Utilizing wreath products to construct a sequence of Cayley Graphs with logarithmic diameter by Preston Smith
- Iterated semi-direct product of the integers modulo two by Matthew Aivazian
- Subspace methods in the eigenvalue problem by Yasmine Balkis
- A master's thesis on the Wirtinger presentation by Chris Thiel
- A master's thesis on diameters of Cayley graphs by Keith D'Souza
- A master's thesis on Krull dimension by Carlos Arcos
- A master's thesis on Ramanujan graphs by Mustafa El-Sanfaz

## Presentations

## Other, random stuff

- A group of Cal State LA students on the My Favorite Theorem podcast
- Silly math videos I've made
- Bizarre and/or mediocre songs I've made

I graduated from Johns Hopkins University in May 2005. My thesis advisor was Dr. Richard Wentworth.

This website was last updated in May 2022.