On the Matching Spectrum of Rotagraphs

Abstract

The matching polynomial of the rotagraph UM with M monomer units and one linking edge between the units is considered, with particular attention paid to its zeros. It has been found that the matching spectrum of an infinite rotagraph has, like its characteristic spectrum, a band-like structure. The factorization of the matching polynomial of UM has been derived, the result being fully analogous to the factorization of the corresponding characteristic polynomial. These results can be used for quick and easy evaluation of the matching spectrum of infinite and finite UM of any size. For a certain class of UM, having an acyclic monomer unit, the matching and the characteristic bands coincide. The matching and the characteristic bands of some particular rotagraphs are evaluated.