The second path matrix S(G) collects all the second paths in the graph G. Its characteristic polynomial shows some regularity in several particular graphs, such as paths, cycles, stars and complete ...

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 ...

We introduce a many-variable version of the f-polynomial and h-polynomial associated to a finite simplicial complex. In this context the h-polynomial is actually a rational function. We establish ...