A. Erey

activity

20132023

x

-colorings of

4

-chromatic graphs

8 citations · 26 across the 13 of their papers we have counts for

collaborators

15 papers

math.CO2023

Spreading in graphs

Boštjan Brešar, Tanja Dravec, Aysel Erey +1

Several concepts that model processes of spreading (of information, disease, objects, etc.) in graphs or networks have been studied. In many contexts, we assume that some vertices…

math.CO2021

On the average order of a dominating set of a forest

Aysel Erey

We show that the average order of a dominating set of a forest graph $G$ on $n$ vertices with no isolated vertices is at most $2 n /3$ . Moreover, the equality is achieved if and only…

math.CO2021★ 3 cited

Maximal distance spectral radius of 4-chromatic planar graphs

Aysel Erey

We show that the kite graph $K_{4}^{(n)}$ uniquely maximizes the distance spectral radius among all connected $4$ -chromatic planar graphs on $n$ vertices.

math.CO2019

Tomescu's graph coloring conjecture for $ℓ$ -connected graphs

John Engbers, Aysel Erey, Jacob Fox +1

Let $P_{G} (k)$ be the number of proper $k$ -colorings of a finite simple graph $G$ . Tomescu's conjecture, which was recently solved by Fox, He, and Manners, states that $P_G(k) \le k!…

math.CO2019★ 5 cited

Uniform Length Dominating Sequence Graphs

Aysel Erey

A sequence of vertices $(v_{1}, \dots, v_{k})$ of a graph $G$ is called a {\it dominating closed neighborhood sequence} if ${v_{1}, \dots, v_{k}}$ is a dominating set of $G$ an…

math.CO2017

Characterization and enumeration of 3-regular permutation graphs

Aysel Erey, Zachary Gershkoff, Amanda Lohss +1

A permutation graph is a graph that can be derived from a permutation, where the vertices correspond to letters of the permutation, and the edges represent inversions. We provide a…

math.CO2016

A note on the real part of complex chromatic roots

Jason Brown, Aysel Erey

A {\em chromatic root} is a root of the chromatic polynomial of a graph. While the real chromatic roots have been extensively studied and well understood, little is known about the…

math.CO2016

New Bounds for Chromatic Polynomials and Chromatic Roots

Jason Brown, Aysel Erey

If $G$ is a $k$ -chromatic graph of order $n$ then it is known that the chromatic polynomial of $G$ , $π (G, x)$ , is at most $x (x - 1) \dots (x - (k - 1)) x^{n - k} = (x)_{↓ k} x^{n - k}$ …

math.CO2016

Restraints Permitting the Largest Number of Colourings

Jason Brown, Aysel Erey

A \textit{restraint} $r$ on $G$ is a function which assigns each vertex $v$ of $G$ a finite set of forbidden colours $r (v)$ . A proper colouring $c$ of $G$ is said to be \textit{per…

math.CO2016

On the real roots of $σ$ -Polynomials

Jason Brown, Aysel Erey

The $σ$ -polynomial is given by $σ (G, x) = \sum_{i = χ (G)}^{n} a_{i} (G) x^{i}$ , where $a_{i} (G)$ is the number of partitions of the vertices of $G$ into $i$ nonempty independent sets…

math.CO2016★ 6 cited

Extremal Restraints for Graph Colourings

Jason I. Brown, Aysel Erey, Jian Li

A {\em restraint} on a (finite undirected) graph $G = (V, E)$ is a function $r$ on $V$ such that $r (v)$ is a finite subset of $N$ ; a proper vertex colouring $c$ of $G$ is…

math.CO2016★ 8 cited

Maximizing the number of $x$ -colorings of $4$ -chromatic graphs

Aysel Erey

Let $C_{4} (n)$ be the family of all connected $4$ -chromatic graphs of order $n$ . Given an integer $x \geq 4$ , we consider the problem of finding the maximum number of $x$ -co…

math.CO2016

On the maximum number of colorings of a graph

Aysel Erey

Let $C_{k} (n)$ be the family of all connected $k$ -chromatic graphs of order $n$ . Given a natural number $x \geq k$ , we consider the problem of finding the maximum number of…

math.CO2016★ 4 cited

On the Wiener index, distance cospectrality and transmission regular graphs

Aida Abiad, Boris Brimkov, Aysel Erey +5

In this paper, we investigate various algebraic and graph theoretic properties of the distance matrix of a graph. Two graphs are $D$ -cospectral if their distance matrices have the…

math.CO2013

On the roots of $σ$ -polynomials

Jason Brown, Aysel Erey

Given a graph $G$ of order $n$ , the $σ$ - $p o l y n o mia l$ of $G$ is the generating function $σ (G, x) = \sum a_{i} x^{i}$ where $a_{i}$ is the number of partitions of the vertex set of $G$ …

Spreading in graphs

On the average order of a dominating set of a forest

Maximal distance spectral radius of 4-chromatic planar graphs

Tomescu's graph coloring conjecture for ℓ-connected graphs

Uniform Length Dominating Sequence Graphs

Characterization and enumeration of 3-regular permutation graphs

A note on the real part of complex chromatic roots

New Bounds for Chromatic Polynomials and Chromatic Roots

Restraints Permitting the Largest Number of Colourings

On the real roots of σ-Polynomials

Extremal Restraints for Graph Colourings

Maximizing the number of x-colorings of 4-chromatic graphs

On the maximum number of colorings of a graph

On the Wiener index, distance cospectrality and transmission regular graphs

On the roots of σ-polynomials

Tomescu's graph coloring conjecture for $ℓ$ -connected graphs

On the real roots of $σ$ -Polynomials

Maximizing the number of $x$ -colorings of $4$ -chromatic graphs

On the roots of $σ$ -polynomials