Cospectral Graphs and Regular Orthogonal Matrices of Level 2

[摘要] For a graph $\Gamma$ with adjacency matrix $A$, we consider a switching operation that takes $\Gamma$ into a graph $\Gamma'$ with adjacency matrix $A'$, defined by $A'=Q^\top A Q$, where $Q$ is a regular orthogonal matrix of level $2$ (that is, $Q^\top Q=

[学科分类] 离散数学和组合数学

[关键词] Cospectral graphs;Orthogonal matrices;Switching