W. Haemers

activity

20082026

most citedRegular graphs with maximal energy per vertex

9 citations · 16 across the 23 of their papers we have counts for

collaborators

33 papers

math.CO2026

On perfect matchings, edge-colourings and eigenvalues of cubic graphs

Willem H. Haemers

We discuss the question whether the existence of perfect matchings in a cubic graph can be seen from the spectrum of its adjacency matrix. For regular graphs in general and for thr…

math.CO2025

Thin divisible designs graphs: an interplay between fixed-point free involutions of $(v, k, λ)$ -graphs and symmetric weighing matrices

Sergey Goryainov, Willem H. Haemers, Elena V. Konstantinova +1

In this paper, we illustrate important aspects of the interplay between weighing matrices, $(v, k, λ)$ -graphs with fixed-point free involutions, and signed graphs with an orthogonal…

math.CO2024

Divisible design graphs from the symplectic graph

Bart De Bruyn, Sergey Goryainov, Willem Haemers +1

A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a (group) divisible design. Divisible design graphs were introduced in 2011 as a generalization…

math.CO2023

Cospectrality results for signed graphs with two eigenvalues unequal to $\pm 1$

Willem H. Haemers, Hatice Topcu

Recently the collection $G$ of all signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to $\pm 1$ has been determined. Here we investigate $…

math.CO2023

Cospectral mates for generalized Johnson and Grassmann graphs

Aida Abiad, Jozefien D'haeseleer, Willem H. Haemers +1

We provide three infinite families of graphs in the Johnson and Grassmann schemes that are not uniquely determined by their spectrum. We do so by constructing graphs that are cospe…

math.CO2023

The signed graphs with two eigenvalues unequal to $\pm 1$

Willem Haemers, Hatice Topcu

We complete the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to $\pm 1$ . The unsigned graphs and the disconnected, th…

math.CO2021

On signed graphs with at most two eigenvalues unequal to $\pm 1$

Willem H. Haemers, Hatice Topcu

We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to 1 or -1. Here we deal with the…

math.CO2021

Graph toughness from Laplacian eigenvalues

Xiaofeng Gu, Willem H. Haemers

The toughness $t (G)$ of a graph $G = (V, E)$ is defined as $t (G) = min {\frac{∣ S ∣}{c ( G - S )}}$ , in which the minimum is taken over all $S \subset V$ such that $G - S$ is disconnected, wher…

math.CO2021

Hoffman's ratio bound

Willem H. Haemers

Hoffman's ratio bound is an upper bound for the independence number of a regular graph in terms of the eigenvalues of the adjacency matrix. The bound has proved to be very useful a…

math.CO2021

Spectra of strongly Deza graphs

Saieed Akbari, Willem H. Haemers, Mohammad Ali Hosseinzadeh +3

A Deza graph $G$ with parameters $(n, k, b, a)$ is a $k$ -regular graph with $n$ vertices such that any two distinct vertices have $b$ or $a$ common neighbours. The children $G_{A}$ and…

math.CO2020

Universal spectra of the disjoint union of regular graphs

Willem H. Haemers, Mohammad Reza Oboudi

A universal adjacency matrix of a graph $G$ with adjacency matrix $A$ is any matrix of the form $U = α A + β I + γ J + δ D$ with $α \neq = 0$ , where $I$ is the identity matrix, $J$ is the…

math.CO2020

Spectral symmetry in conference matrices

Willem H. Haemers, Leila Parsaei Majd

A conference matrix of order $n$ is an $n \times n$ matrix $C$ with diagonal entries $0$ and off-diagonal entries $\pm 1$ satisfying $C C^{⊤} = (n - 1) I$ . If $C$ is symmetric, then $C$ …

math.CO2020

On sign-symmetric signed graphs

Ebrahim Ghorbani, Willem H. Haemers, Hamid Reza Maimani +1

A signed graph is said to be sign-symmetric if it is switching isomorphic to its negation. Bipartite signed graphs are trivially sign-symmetric. We give new constructions of non-bi…

math.CO2020

On NP-hard graph properties characterized by the spectrum

Omid Etesami, Willem H. Haemers

Properties of graphs that can be characterized by the spectrum of the adjacency matrix of the graph have been studied systematically recently. Motivated by the complexity of these…

math.CO2019

Cospectral pairs of regular graphs with different connectivity

Willem H. Haemers

For vertex and edge connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.

math.CO2018

On the spectral characterization of mixed extensions of $P_{3}$

Willem H. Haemers, Sezer Sorgun, Hatice Topcu

A mixed extension of a graph $G$ is a graph $H$ obtained from $G$ by replacing each vertex of $G$ by a clique or a coclique, whilst two vertices in $H$ corresponding to distinct ve…

math.CO2018★ 4 cited

The chromatic index of strongly regular graphs

Sebastian M. Cioaba, Krystal Guo, Willem H. Haemers

We determine (partly by computer search) the chromatic index (edge-chromatic number) of many strongly regular graphs (SRGs), including the SRGs of degree $k \leq 18$ and their comp…

math.CO2018

Deza graphs with parameters $(n, k, k - 1, a)$ and $β = 1$

Sergey Goryainov, Willem H. Haemers, Vladislav V. Kabanov +1

A Deza graph with parameters $(n, k, b, a)$ is a $k$ -regular graph with $n$ vertices in which any two vertices have $a$ or $b$ ( $a \leq b$ ) common neighbours. A Deza graph is strictly…

math.CO2018★ 1 cited

Graph switching, 2-ranks, and graphical Hadamard matrices

Aida Abiad, Steve Butler, Willem H. Haemers

We study the behaviour of the 2-rank of the adjacency matrix of a graph under Seidel and Godsil-McKay switching, and apply the result to graphs coming from graphical Hadamard matri…

math.CO2017

Spectral characterization of mixed extensions of small graphs

Willem H. Haemers

A mixed extension of a graph $G$ is a graph $H$ obtained from $G$ by replacing each vertex of $G$ by a clique or a coclique, where vertices of $H$ coming from different vertices of…

math.CO2017

Signed graphs cospectral with the path

Saieed Akbari, Willem H. Haemers, Hamid Reza Maimani +1

A signed graph $Γ$ is said to be determined by its spectrum if every signed graph with the same spectrum as $Γ$ is switching isomorphic with $Γ$ . Here it is proved that the path $P…

math.CO2016★ 2 cited

The graphs with all but two eigenvalues equal to $- 2$ or $0$

Sebastian M. Cioaba, Willem H. Haemers, Jason R. Vermette

We determine all graphs for which the adjacency matrix has at most two eigenvalues (multiplicities included) not equal to $- 2$ , or $0$ , and determine which of these graphs are dete…

math.CO2015

On the spectral characterization of pineapple graphs

Hatice Topcu, Sezer Sorgun, Willem H. Haemers

The pineapple graph $K_{p}^{q}$ is obtained by appending $q$ pendant edges to a vertex of a complete graph $K_{p}$ ( $q \geq 1, p \geq 3$ ). Zhang and Zhang ["Some graphs determined by th…

math.CO2014

Switched symplectic graphs and their 2-ranks

Aida Abiad, Willem H. Haemers

We apply Godsil-McKay switching to the symplectic graphs over $F_{2}$ with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases af…

On perfect matchings, edge-colourings and eigenvalues of cubic graphs

Thin divisible designs graphs: an interplay between fixed-point free involutions of (v,k,λ)-graphs and symmetric weighing matrices

Divisible design graphs from the symplectic graph

Cospectrality results for signed graphs with two eigenvalues unequal to ±1

Cospectral mates for generalized Johnson and Grassmann graphs

The signed graphs with two eigenvalues unequal to ±1

On signed graphs with at most two eigenvalues unequal to ±1

Graph toughness from Laplacian eigenvalues

Hoffman's ratio bound

Spectra of strongly Deza graphs

Universal spectra of the disjoint union of regular graphs

Spectral symmetry in conference matrices

On sign-symmetric signed graphs

On NP-hard graph properties characterized by the spectrum

Cospectral pairs of regular graphs with different connectivity

On the spectral characterization of mixed extensions of P3​

The chromatic index of strongly regular graphs

Deza graphs with parameters (n,k,k−1,a) and β=1

Graph switching, 2-ranks, and graphical Hadamard matrices

Spectral characterization of mixed extensions of small graphs

Signed graphs cospectral with the path

The graphs with all but two eigenvalues equal to −2 or 0

On the spectral characterization of pineapple graphs

Switched symplectic graphs and their 2-ranks

Thin divisible designs graphs: an interplay between fixed-point free involutions of $(v, k, λ)$ -graphs and symmetric weighing matrices

Cospectrality results for signed graphs with two eigenvalues unequal to $\pm 1$

The signed graphs with two eigenvalues unequal to $\pm 1$

On signed graphs with at most two eigenvalues unequal to $\pm 1$

On the spectral characterization of mixed extensions of $P_{3}$

Deza graphs with parameters $(n, k, k - 1, a)$ and $β = 1$

The graphs with all but two eigenvalues equal to $- 2$ or $0$