Matching Polynomials of Regular Chain-Type Graphs

In this article we describe an algorithm that allows us to recursively construct the matching polynomials of what we call “regular chain-type graphs”. These graphs are obtained from a fixed base graph by linking several copies in a linear fashion, the links being obtained by joining two consecutive copies at prescribed vertices. Loops obtained by closing these chains are also studied. Finally, a method to compute the growth rate of the Hosoya index is presented. The proposed methods are applicable to chain-type molecular structures, providing insights into their chemical properties. © 2026, University of Kragujevac, Faculty of Science. All rights reserved.