arXiv subjects
Publications and source records attributed to Jozefien D'haeseleer.
A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this paper we give some sufficient and necessary conditions for a Neumaier graph to be strongly regular. Further we show that there does not exist Neumaier graphs with exactly four distinct eigenvalues. We also determine the Neumaier graphs with smallest eigenvalue -2.
In this paper, we analyze the structure of maximal sets of $k$-dimensional spaces in $\mathrm{PG}(n,q)$ pairwise intersecting in at least a $(k-2)$-dimensional space, for $3 \leq k\leq n-2$. We give an overview of the largest examples of these sets with size more than $f(k,q)=\max\{3q^4+6q^3+5q^2+q+1,θ_{k+1}+q^4+2q^3+3q^2\}$.
We determine the chromatic number of some graphs of flags in buildings of type $A_4$, namely of the Kneser graphs of flags of type $\{2,4\}$ in the vector spaces $GF(q)^5$ for $q\geq3$, and of the Kneser graph of flags of type $\{2,3\}$ in the vector spaces $GF(q)^5$ for large $q$.
Let $V$ be a $(d+1)$-dimensional vector space over a field $\mathbb{F}$. Sesquilinear forms over $V$ have been largely studied when they are reflexive and hence give rise to a (possibly degenerate) polarity of the $d$-dimensional projective space PG$(V)$. Everything is known in this case for both degenerate and non-degenerate reflexive forms if $\mathbb{F}$ is either ${\mathbb{R}}$, ${\mathbb{C}}$ or a finite field ${\mathbb{F}}_q$. In this paper we consider degenerate, non-reflexive sesquilinear forms of $V=\mathbb{F}_{q^n}^3$. We will see that these forms give rise to degenerate correlations of PG$(2,q^n)$ whose set of absolute points are, besides cones, the (possibly degenerate) $C_F^m$-sets. In the final section we collect some results from the huge work of B.C. Kestenband regarding what is known for the set of the absolute points of correlations in PG$(2,q^n)$ induced by a non-degenerate, non-reflexive sesquilinear form of $V=\mathbb{F}_{q^n}^3$.
In this paper, we study translation hyperovals in PG$(2,q^k)$. The main result of this paper characterises the point sets defined by translation hyperovals in the André/Bruck-Bose representation. We show that the affine point sets of translation hyperovals in PG$(2,q^k)$ are precisely those that have a scattered $\mathbb{F}_2$-linear set of pseudoregulus type in PG$(2k-1,q)$ as set of directions. This correspondence is used to generalise the results of Barwick and Jackson who provided a characterisation for translation hyperovals in PG$(2,q^2)$.
In this article, we study degree one Cameron-Liebler sets of generators in all finite classical polar spaces, which is a particular type of a Cameron-Liebler set of generators in this polar space, [9]. These degree one Cameron-Liebler sets are defined similar to the Boolean degree one functions, [15]. We summarize the equivalent definitions for these sets and give a classification result for the degree one Cameron-Liebler sets in the polar spaces W(5,q) and Q(6,q).