Design switching on graphs

2025/08/15 by Ferdinand Ihringer, Ihringer, Ferdinand, Robin Simoens +1
Mathematics · #math.CO

paper · pdf · doi:10.48550/arxiv.2508.11523

30 pages, revisions thanks to referees

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

We show that each (r, lambda)-design yields a class of switching methods that can be used to produce cospectral graphs. We use this to explain several specific switching methods such as Godsil-McKay (GM) switching and Wang-Qiu-Hu (WQH) switching.

Citations

• Counting cospectral graphs obtained via switching
• Switching methods of level 2 for the construction of cospectral graphs
• Pseudo-Geometric Strongly Regular Graphs with a Regular Point
• Strongly regular graphs satisfying the 4-vertex condition
• New Strongly Regular Graphs from Finite Geometries via Switching
• A Switching for all Strongly Regular Collinearity Graphs From Polar\n Spaces

Related

• Switching methods of level 2 for the construction of cospectral graphs
• Switching graphs and Hadamard matrices
• A switching method for constructing cospectral gain graphs
• Counting cospectral graphs obtained via switching
• Godsil-McKay switchings for gain graphs