A Characterization of Walk-Matrix Equivalence at Corank Two via Reciprocal WQH Switching

Chaochao Zhu, Qin Yue

Let $G$ be a graph of order $n$ with adjacency matrix $A_G$, let $\mathbf{e}$ denote the all-one vector, and let$W_G=[\mathbf{e},A_G\mathbf{e},\dots ,A_G^{n-1}\mathbf{e}]$ be its walk…