Ting-Ting Wang

The Critical Polynomials of Simple Connected Graphs

Let $ G $ be a connected graph with $ n $ vertices and adjacency matrix $A(G)$. The critical polynomial $d_G(x_1, \ldots, x_n) $ is a degree-$n$ multivariate polynomial defined as the determinant of the matrix $M_G(x_1, \ldots, x_n) $, where \[M_G(x_1,\ldots,x_n) = \operatorname{Diag}(x_1, \ldots, x_n) - A(G).\] For an...