Merrifield-simmons Index And Hosoya Index Of Some Graphs

The oldest number theory has a very wide range of application. In this paper, we use the relation between Fibonacci sequence, Lucas sequence and independent set, matching number in graph theory and chemical stability, boiling point, to determine bounds of Merrifield-Simmons index or Hosoya index in four graphs. Merrifield-Simmons index and Hosoya index are two very important and popular index in chemical graph theory. Whose index sequences relate to properties of the molecular structure such as molecular stability, boiling point and so on. The studying on topological structure and topological properties of chemical molecules, has important application in making new compounds and new drugs.In this paper, some results with respect to Merrifield-Simmons index and Hosoya index of tree-type hexagonal systems, graphs Q(Pn;Cs1,Cs2,...,Csn), Q(Cn;Cs1,Cs2,...,Csn) and Q(Wn;Cs1,Cs2,...,Csn are shown. Using these results, the tree-type hexagonal system, graphs Q(Pn;Cs1,Cs2,...,Csn), Q(Cn;Cs1, Cs2,..., Csn) and Q(Wn; Cs1,Cs2,..., Csn) with larger and lower bound of Merri field-Simmons index or Hosoya index are determined.