The Topological Indices of Two Types Tricyclic Graphs 

Author  WanHua 
Tutor  RenHaiZhen 
School  Qinghai Normal 
Course  Basic mathematics 
Keywords  MerrifieldSimmons index Hosoya index Wiener index tricyclicgraphAMS subject classification (2000)C15 05C60 
CLC  O157.5 
Type  Master's thesis 
Year  2012 
Downloads  21 
Quotes  0 
Let G=(V, E) be a simple connected graph with the vertex set V(G) and the edge set E(G). V(G)=nand E(G)=m denote the number of edges and vertices, respectively. A tricyclic graph is a connected graph with n vertices and n+2edges.Let S be a subset of the vertex set of G, if any two vertices in S are not adjacent then S is a independent vertex set of G. The MerrifieldSimmons index of the graph G, denoted by i(G), is the number of the independent vertex set of G. Let m(G, k) be the number of kmatchings of graph G. Then the Hosoya index of G is defined as The Wiener index W(G) of G is the sum of distances between all pairs of vertices in G, i.e where dG(u,v) is the distance between vertices u and v in G.MerrifieldSimmons index, Hosoya index and Wiener index are three typical Topological indices. They have been widely investigated in mathematics and chemistry as well, and the Wiener index has been successfully used in theoretical chemistry for quantitative structureproperty relations(QSPR) and quantitative structureproperty relations(QSAR), and also in studying communication networks.In this paper, we study the MerrifieldSimmons index, the Hosoya index and the Wiener index of some tricyclic graphs which contain three cycles. Firstly, we give some graph transformations, and then by these graph transformations, we characterize graphs with the largest, the second smallest Hosoya index, the smallest MerrifieldSimmons index and the smallest, the second smallest Wiener index, respectively. At the end of this paper, we get a part of results on the MerrifieldSimmons index, Hosoya index and Wiener index of some tricyclic graphs which contain four cycles.