The Characteristic Polynomial
Chris D. Godsil · 2017
The adjacency matrix A = A ( G ) of the graph G is the n × n matrix with ij -entry equal to 1 if the i -th vertex of G is adjacent to the j -th, and equal to 0 otherwise. (We will often identify the vertices of G with the integers 1 to n .) If G ′ is a graph which is isomorphic to G then A ( G ′) is not, in general, equal to A ( G ). However there will be an n × n permutation matrix P such that P A ( G ′ ) P T = A ( G ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137131/3e789cab-79f2-434a-a841-e2acf5146c2d/content/eq107.tif"/>