On the Walks and Bipartite Double Coverings of Graphs with the same Main Eigenspace

Luke Collins, Irene Sciriha

The main eigenvalues of a graph $G$ are those eigenvalues of the $(0,1)$-adjacency matrix $\mathbf{A}$ having a corresponding eigenvector not orthogonal to $\mathbf{j}=(1,\dots ,1)$…