F. Lazebnik

activity

19952026

most citedSpectral and Combinatorial Properties of Some Algebraically Defined Graphs

2 citations · 4 across the 11 of their papers we have counts for

collaborators

13 papers

math.CO2026

Isomorphism Criterion of Monomial Digraphs over Prime Fields

Alexander M. Kodess, Felix Lazebnik, Mikhail Muzychuk

For any Galois field $F_{q}$ with $q$ elements and any positive integers $m$ and $n$ , the directed graph $D (q; m, n)$ has vertex set $F_{q} \times F_{q}$ , and ther…

math.CO2025

Some families of graphs, hypergraphs and digraphs defined by systems of equations

Felix Lazebnik, Ye Wang

The families of graphs defined by a certain type of system of equations over commutative rings have been studied and used since 1990s. This survey presents these families and their…

math.CO2022

On Pappus Configurations in Hall Planes

Felix Lazebnik, Lorinda Leshock

As the finite Hall planes are Non-Desarguesian, the Pappus Theorem does not hold in them. In this paper we state and prove some weaker versions of Pappus's Theorem in Hall planes.

math.CO2021

A New Family of Algebraically Defined Graphs With Small Automorphism Group

Felix Lazebnik, Vladislav Taranchuk

Let $p$ be an odd prime, $q = p^{e}$ , $e \geq 1$ , and $F = F_{q}$ denote the finite field of $q$ elements. Let $f : F^{2} \to F$ and $g: \mathbb{F}^3\to \ma…

math.CO2019

A result on polynomials derived via graph theory

Robert S. Coulter, Stefaan De Winter, Alex Kodess +1

We present an example of a result in graph theory that is used to obtain a result in another branch of mathematics. More precisely, we show that the isomorphism of certain directed…

math.CO2018

A Note on the Isomorphism Problem for Monomial Digraphs

Alex Kodess, Felix Lazebnik

Let $p$ be a prime $e$ be a positive integer, $q = p^{e}$ , and let $F_{q}$ denote the finite field of $q$ elements. Let $m, n$ , $1 \leq m, n \leq q - 1$ , be integers. The monomial dig…

math.CO2018

Diameter of Some Monomial Digraphs

Alex Kodess, Felix Lazebnik, Stephen Smith +1

Let $p$ be a prime, $e$ a positive integer, $q = p^{e}$ , and let $F_{q}$ denote the finite field of $q$ elements. Let $f_{i} : F_{q}^{2} \to F_{q}$ be arbitrary functi…

math.CO2018

Connectivity of some Algebraically Defined Digraphs

Alex Kodess, Felix Lazebnik

Let $p$ be a prime, $e$ a positive integer, $q = p^{e}$ , and let $F_{q}$ denote the finite field of $q$ elements. Let $f_{i} : F_{q}^{2} \to F_{q}$ be arbitrary functi…

math.CO2017★ 2 cited

Spectral and Combinatorial Properties of Some Algebraically Defined Graphs

Sebastian M. Cioabă, Felix Lazebnik, Shuying Sun

Let $k \geq 3$ be an integer, $q$ be a prime power, and $F_{q}$ denote the field of $q$ elements. Let $f_{i}, g_{i} \in F_{q} [X]$ , $3 \leq i \leq k$ , such that $g_i(-X) = -\, g_i…

math.CO2015★ 1 cited

Proof of a conjecture on monomial graphs

Xiang-dong Hou, Stephen D. Lappano, Felix Lazebnik

Let $e$ be a positive integer, $p$ be an odd prime, $q = p^{e}$ , and $F_{q}$ be the finite field of $q$ elements. Let $f, g \in F_{q} [X, Y]$ . The graph $G = G_{q} (f, g)$ is a biparti…

math.CO2014

On the Spectrum of Wenger Graphs

Sebastian M. Cioabă, Felix Lazebnik, Weiqiang Li

Let $q = p^{e}$ , where $p$ is a prime and $e \geq 1$ is an integer. For $m \geq 1$ , let $P$ and $L$ be two copies of the $(m + 1)$ -dimensional vector spaces over the finite field $\mathbb{…

math.CO2013★ 1 cited

Embedding cycles in finite planes

Felix Lazebnik, Keith E. Mellinger, Oscar Vega

We define and study embeddings of cycles in finite affine and projective planes. We show that for all $k$ , $3 \leq k \leq q^{2}$ , a $k$ -cycle can be embedded in any affine plane of order…

math.CO1995

A new series of dense graphs of high girth

Felix Lazebnik, Vasiliy A. Ustimenko, Andrew J. Woldar

Let $k \geq 1$ be an odd integer, $t = ⌊ \frac{k + 2}{4} ⌋$ , and $q$ be a prime power. We construct a bipartite, $q$ -regular, edge-transitive graph $C D (k, q)$ of order $v \l…