Papers › On a question of Haemers regarding vectors in the nullspace of Seidel matrices
On a question of Haemers regarding vectors in the nullspace of Seidel matrices
Saieed Akbari, Sebastian M. Cioabă, Samira Goudarzi, Aidin Niaparast, Artin Tajdini
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
In 2011, Haemers asked the following question: If S is the Seidel matrix of a graph of order n and S is singular, does there exist an eigenvector of S corresponding to 0 which has only ±1 elements? In this paper, we construct infinite families of graphs which give a negative answer to this question. One of our constructions implies that for every natural number N, there exists a graph whose Seidel matrix S is singular such that for any integer vector in the nullspace of S, the absolute value of any entry in this vector is more than N. We also derive some characteristics of vectors in the nullspace of Seidel matrices, which lead to some necessary conditions for the singularity of Seidel matrices. Finally, we obtain some properties of the graphs which affirm the above question.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections