A Research On Two Types Of Graphs About Merrifield-simmons Index And Hosoya Index

Topological indices provide an interesting and powerful tool to study thestructure of molecules and their physicochemical properties．Merrifield-Simmonsindex and Hosoya index are the two valuable topological indices in chemical graphtheory．The Merrifield-Simmons index and Hosoya index are typical examples ofgraph invariants used in mathematical chemistry for quantifying relevant details ofmolecular structure．The Merrifield-Simmons index of a graph G is defined as thetotal number of the independent sets of the graph G and the Hosoya index of agraph G is defined as the total number of the matchings of the graph G．These twotopological indices has important application in making new compounds and newdrugs．So far，many results have been achieved on them．The mathematical researchabout them mainly focuses on tiling problem、enumerations、matchings counting、independent sets counting and respective ordings problem，etc．In this paper，firstly，based on the study of compound graphs、hexagonal chainsand so on，with respect to Merrifield-Simmons index and Hosoya index，we constructtwo classes special graphsG~i_n and H~i_n，Secondly，study the Merrifield-Simmonsindices and Hosoya indices of these graphs，and the recurrence formulas are given．...