Graph reduction techniques and the multiplicity of the Laplacian eigenvalues

Asghar Bahmani, Dariush Kiani

Let $M=[m_{ij}]$ be an $n\times m$ real matrix, $\rho$ be a nonzero real number, and $A$ be a symmetric real matrix. We denote by $D(M)$ the $n\times n$ diagonal matrix $diag(\sum_{j=…