Alexander L. Gavrilyuk

activity

20102024

most citedDerivation of Cameron-Liebler line classes

30 citations · 43 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2024

A characterization of the Grassmann graphs: one missing case

Jack H. Koolen, Chenhui Lv, Alexander L. Gavrilyuk

We prove that the Grassmann graphs $J_{2} (2 D + 3, D)$ , $D \geq 3$ , are characterized by their intersection numbers, which settles one of the few remaining cases.

math.CO2018★ 1 cited

On a characterization of the Grassmann graphs

Alexander L. Gavrilyuk, Jack H. Koolen

In 1995, Metsch showed that the Grassmann graph $J_{q} (n, D)$ of diameter $D \geq 3$ is characterized by its intersection numbers with the following possible exceptions: (-) $n = 2 D$ or…

math.CO2018★ 8 cited

Cameron-Liebler line classes in $PG (3, 5)$

Alexander L. Gavrilyuk, Ilia Matkin

We complete a classification of Cameron-Liebler line classes in $PG (3, 5)$ , and show in a uniform way all non-existence results for those in $PG (3, q)$ , $q \leq 5$ .

math.CO2016★ 30 cited

Derivation of Cameron-Liebler line classes

Alexander L. Gavrilyuk, Ilia Matkin, Tim Penttila

We construct a new infinite family of Cameron-Liebler line classes in $P G (3, q)$ with parameter $x = \frac{q ^{2} + 1}{2}$ for all odd $q$ .

math.CO2015★ 2 cited

A characterization of the graphs of bilinear $(d \times d)$ -forms over $F_{2}$

Alexander L. Gavrilyuk, Jack H. Koolen

The bilinear forms graph denoted here by $B i l_{q} (e \times d)$ is a graph defined on the set of $(e \times d)$ -matrices ( $e \geq d$ ) over $F_{q}$ with two matrices being adjacent…

math.CO2014

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

Alexander L. Gavrilyuk, Jack H. Koolen

Let $Γ$ be a $Q$ -polynomial distance-regular graph with diameter at least $3$ . Terwilliger (1993) implicitly showed that there exists a polynomial, say $T (λ) \in C [λ]$ , of…

math.CO2013

On the Godsil -- Higman necessary condition for equitable partitions of association schemes

Alexander L. Gavrilyuk, Ivan Yu. Mogilnykh

In the monograph 'Association schemes', C. Godsil derived a necessary condition for equitable partitions of association schemes and noticed that it could be used to show that certa…

math.CO2012★ 1 cited

A note on Cameron - Liebler line classes in PG(n,4)

Alexander L. Gavrilyuk, Ivan Y. Mogilnykh

A {\it Cameron -- Liebler line class} $L$ with parameter $x$ is a set of lines of projective geometry $P G (3, q)$ such that each line of $L$ meets exactly $x(q+1)+q^2-1…

math.CO2010★ 1 cited

On a Koolen -- Park inequality and Terwilliger graphs

Alexander Gavrilyuk

J.H. Koolen and J. Park have proved a lower bound for intersection number $c_{2}$ of a distance-regular graph $Γ$ . Moreover, they showed that the graph $Γ$ which attains the equality…

A characterization of the Grassmann graphs: one missing case

On a characterization of the Grassmann graphs

Cameron-Liebler line classes in PG(3,5)

Derivation of Cameron-Liebler line classes

A characterization of the graphs of bilinear (d×d)-forms over F2​

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

On the Godsil -- Higman necessary condition for equitable partitions of association schemes

A note on Cameron - Liebler line classes in PG(n,4)

On a Koolen -- Park inequality and Terwilliger graphs

Cameron-Liebler line classes in $PG (3, 5)$

A characterization of the graphs of bilinear $(d \times d)$ -forms over $F_{2}$