Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

It is known that there exist many pairs of nonisomorphic graphs which have the same set of eigenvalues, even when counting multiplicities. Such graphs have identical characteristic polynomials (of ...

In engineering and applied mathematics, polynomial systems arise whose solution sets contain components of different dimensions and multiplicities. In this article we present algorithms, based on ...