Mike Krebs

College of Natural & Social Sciences

Department of Mathematics

Office STF317

Phone

x3-2150

[email protected]

Teaching

Class websites

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