In linear algebra, every square matrix is associated with a characteristic polynomial. This polynomial encodes several important properties of the matrix, most notably its eigenvalues, its determinant and its trace.
The characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix. It is a graph invariant, though it is not complete: the smallest pair of non-isomorphic graphs with the same characteristic polynomial have five nodes.
Read more about Characteristic Polynomial: Motivation, Formal Definition, Examples, Properties, Characteristic Polynomial of A Product of Two Matrices