My Research Interests and Collaborations

I have had the honour and pleasure of completing my M.Sc. Math. under the supervision of Professor Abraham Berman and have now started my Ph.D.

I've also done some work with my friends Yulia Bougaev, Natan Keller and Gregory (Grisha) Shapiro, some of it is listed below.

Currently I'm working on/thinking about/reading more about:

  • Matrices of graphs.
  • Application of various inequalities to estimate graphs spectra.
  • Laplacians symmetries of various objects.
  • Homological methods in combinatorics.
  • Appilcations of optimization techniques in combinatorics.
  • Isoperimetric problems on graphs.
  • Variational calculus.

My Publications and Preprints

I'll be happy to provide reprints or preprints at request - just drop me a line if you want anything...

(1) Felix Goldberg, "On completely positive graphs and their complements", Linear Algebra and its Applications, vol. 371 (2003), pp. 45-51.

A preprint version is available.

The final version can be accessed online through ScienceDirect (requires subscription).

(2) Felix Goldberg and Gregory Shapiro, "The Merris index of a graph", Electronic Journal of Linear Algebra, vol. 10 (2003), pp. 212-222.

Available here.

(3) Felix Goldberg, "On quasi-strongly regular graphs", Linear and Miltilinear Algebra, vol. 54 (2006), no. 6. pp. 437-451.

(4) Felix Goldberg, "Bounding the gap between extremal Laplacian eigenvalues of graphs", Linear Algebra and its Applications, vol. 416 (2006), pp. 68-74.

 (5) "The deck ratio and self-repairing graphs" (Joint work with Yulia Bugaev), submitted To Electronic Journal of Combinatorics.

(6) "Bounds on the (\alpha+1)-th Laplacian eigenvalue of a graph", submitted to Linear Algebra and its Applications.
 

My Talks

January 2004: Quasi-Strongly Regular Graphs, Combinatorics Seminar at Bar-Ilan University, Ramat-Gan, Israel

May 2004: Quasi-Strongly Regular Graphs, Combinatorics Seminar at the Hebrew University, Jerusalem, Israel

January 2005: Laplacian Eigenvalues of Graphs and Reverse Cauchy-chwarz Inequalities, 13th Haifa Matrix Theory Conference, Technion, Haifa, Israel
 

My Thesis

Laplacians of Graphs, Quasi-Strongly Regular Graphs and Completely Positive Graphs

Some Open Problems That Interest Me (still undone, ah, "time, it takes time...")

Here I list some major open problems which I from time to time attempt to attack, either on my own or together with friends.

Frankl's conjecture. A concise survey by Douglas West.

Vizings's conjecture.

Fu, Huang and Rodger's conjecture that a (k,g)-cage is k-connected.

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Last Updated October 3, 2006