On Orderings of Some Graphs by the Extreme Roots of their Graph Polynomials

Various aspects of combinatorial information concerning a graph is stored in the coefficients of a specific graph polynomial, so represented also by the roots of such graph polynomial. It is natural to ask about the nature and location of the roots. In this paper, the orderings of some graphs by the minimum real roots of their adjoint polynomials are obtained. Moreover, the orderings of some trees by the maximum roots of their characteristic polynomials (resp. their matching polynomials) are attained as well.