Archimedean Tilings And Binary Hamming Graphs

In chemical graph theory, several molecular topological indices are basedon vertex distances. Wiener number which conceived by Wiener in 1947 is oneof them. Pepole have studied Wiener number for more than half of a centuryand obtain a series of results. In this thesis, we consider the Wiener index ofseveral subgraphs of some Archimedean tilings.The whole dissertation includes three chapters. The first chapter is intro-duction. In the second chapter, we restrict attention to Archimedean tilings.We find all the tilings corresponding to binary Hamming graph(say binaryHamming tiling) in Archimedean tilings. Actually they are only four suchtilings:(4.4.4.4),(6.6.6), (4.8.8)and(4.6.12). Then we extend the method tocomputing the Wiener number of benzenoid system to these four tilings, andcompute some examples.In the third chapter , we make a brief introduction on the extremal general-ized polyomino chains on Wiener number. For any generalized polyomino chainT_n∈(?)_n,denote W(T_n)the wiener number of T_n．We show that for any gener-alized polyomino chain T_n∈(?)_n,when n is odd,W(H_n)≤W(T_n)≤W(L_n),with the left equalities holding only if T_n=H_n,and the right equalities hold-ing only if T_n=L_n,when n is even,W(H'_n)≤W(T_n)≤W(L_n),with the leftequalities holding only if T_n=H'_n,the right equalities holding only if T_n=L_n,where L_n is the linear chains,H_n(n is odd)is the helix chains and H'_n(n iseven)will be defined in the article．...