Local operations of combinatorial structures (graphs, Hadamard matrices, codes, designs) that maintain the basic parameters unaltered, have been widely used in the literature under the name of switching. We show an equivalence between two switching methods to construct inequivalent Hadamard matrices, which were proposed by Orrick in 2008, and the switching method for constructing cospectral graphs which was introduced by Godsil and McKay in 1982.
Local operations of combinatorial structures (graphs, Hadamard matrices, codes, designs) that maintain the basic parameters unaltered, have been widely used in the literature under the name of switching. We show an equivalence between two switching methods to construct inequivalent Hadamard matrices, which were proposed by Orrick in 2008, and the switching method for constructing cospectral graphs which was introduced by Godsil and McKay in 1982.
Open Problems on Rank Metric Codes
| # | Наименование новости | Тональность | Информативность | Дата публикации |
|---|---|---|---|---|
| 1 | Rank-metric codes over arbitrary fields: Bounds and constructions | 0 | 8.4 | 10-08-2026 |
| 2 | Perfect Hermitian rank-metric codes | 0 | 9.18 | 01-07-2026 |
| 3 | Paint cost spectrum of perfect k-ary trees | 0 | 5.15 | 28-01-2026 |
| 4 | Scramble number and tree-cut decompositions | 0 | 9.18 | 21-04-2026 |
| 5 | A note on Cayley nut graphs whose degree is divisible by four | 0 | 11.62 | 03-02-2026 |
| 6 | Scattered polynomials: an overview on their properties, connections and applications | 0 | 9.4 | 22-05-2026 |
| 7 | The fibre--sum of graphs | 0 | 3.28 | 10-08-2026 |
| 8 | Edge criticality in signed graphs admitting a Roman dominating function | 0 | 8.11 | 26-02-2026 |
| 9 | Equitable Domination in Turiyam Graphs with Network Applications [version 1; peer review: 3 approved] | 0 | 7 | 01-06-2026 |
| 10 | The Möbius–Kantor graph is a faithful unit-distance graph | 0 | 13.24 | 12-03-2026 |