Alexander Gavrilyuk

I am a JSPS Postdoctoral Fellow working with Akihiro Munemasa at GSIS, Tohoku University, Japan.

I also work at Department of Algebra and Topology of N.N. Krasovsky Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, Russia.

You might be interested in my CV pdf.

Research

My main research interests are in algebraic combinatorics: distance-regular graphs (and graph theory in general), finite geometry, design theory.

Below you can find some selected papers (see CV for all publications), a list of current projects and pdf-slides of some talks.

Selected papers

On Krein graphs without triangles pdf

Doklady Mathematics (2005), no. 72, 591-594

Distance-regular graphs with intersection arrays {52,35,16;1,4,28} and {69,48,24;1,4,46} do not exist pdf

Designs, Codes and Cryptography. 65 (2012), no. 1-2, 49–54

On perfect 2-colorings of Johnson graphs J(v,3) pdf

Journal of Combinatorial Designs. 21 (2013), no. 6, 232–252

Cameron-Liebler line classes in PG(n,4) pdf

Designs, Codes and Cryptography (accepted)

A modular equality for Cameron-Liebler line classes pdf

Journal of Combinatorial Theory, Series A (accepted)

Work in progress

The distance-regular graphs without 4-claws

The Terwilliger polynomial of a Q-polynomial distance-regular graph and its application
to pseudo-partition graphs

submitted

A note on Q-polynomial distance-regular graphs of type 2

On a characterization of the bilinear forms graphs by their intersection arrays

On a characterization of the Grassmann graphs by their intersection arrays

2-Walk-regular graphs with second largest eigenvalue equal to b_1-1

Some new non-regular graphs with 3 distinct eigenvalues

Completely regular codes with strength one in Johnson graphs J(v,3)

On Deza graphs with 4 distinct eigenvalues

Some Talks

2014

On a Characterization of the Grassmann graphs slides, pdf

Modern Trends in Algebraic Graph Theory (Villanova University, USA)

2014

On Q-polynomial distance-regular graphs of type 2 slides, pdf

Japan Conference on Graph Theory and Combinatorics
(Nihon University, Japan)

2014

On a Characterization of the Bilinear Forms Graphs slides, pdf

Korea-Japan Workshop on Algebra and Combinatorics (KAIST, South Korea)

2013

Cameron-Liebler line classes slides, pdf

Seminar (Tohoku University, Japan)

2012

Perfect 2-colorings of Johnson graphs J(v,3) slides, pdf

Incidence Geometry and Buildings (Ghent University, Belgium)

2011

There exist no distance-regular graphs with intersection arrays {45,30,7;1,2,27}
or {52,35,16;1,4,28} slides, pdf

Geometric and Algebraic Combinatorics (GAC) (Oisterwijk, the Netherlands)