Switching methods of level 2 for the construction of cospectral graphs
A Abiad, N van de Berg, R Simoens - arXiv preprint arXiv:2410.07948, 2024 - arxiv.org
A switching method is a graph operation that results in cospectral graphs (graphs with the
same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most …
same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most …
An infinite class of Neumaier graphs and non-existence results
A Abiad, W Castryck, M De Boeck, JH Koolen… - Journal of Combinatorial …, 2023 - Elsevier
A Neumaier graph is a non-complete edge-regular graph containing a regular clique. A
Neumaier graph that is not strongly regular is called a strictly Neumaier graph. In this work …
Neumaier graph that is not strongly regular is called a strictly Neumaier graph. In this work …
Vertex-transitive Neumaier graphs
M Jazaeri - arXiv preprint arXiv:2408.13722, 2024 - arxiv.org
A graph $\Gamma $ is called edge-regular whenever it is regular and for any two adjacent
vertices the number of their common neighbors is independent of the choice of vertices. A …
vertices the number of their common neighbors is independent of the choice of vertices. A …
Uniform Shared Neighborhood Structures in Edge-Regular Graphs
J DeLeo - arXiv preprint arXiv:2409.00268, 2024 - arxiv.org
A shared neighborhood structure (SNS) in a graph is a subgraph induced by the intersection
of the open neighbor sets of two adjacent vertices. If a SNS is the same for all adjacent …
of the open neighbor sets of two adjacent vertices. If a SNS is the same for all adjacent …
[PDF][PDF] Switching methods for the construction of cospectral graphs
A Abiad, N van de Berg… - … Mathematics Days 2024, 2024 - dmd2024.web.uah.es
An important problem in algebraic graph theory is to decide whether a graph is determined
by the spectrum of its adjacency matrix (see the surveys [10, 11]). In 2003, van Dam and …
by the spectrum of its adjacency matrix (see the surveys [10, 11]). In 2003, van Dam and …