Abstract:

On Fibonacci numbers，there exist some beautifu1 and value conclusions．Here many results are stated．In this paper we obtain the formula of all-factors of the special graph G by means of analyzing method of graphic components and Fibonacci number．By the relation between A(G)and hosoya index of the G without subgraph the relationship betweenandcould be moved to Hosova index for the special graph G．Finally．some special examples for Hosoya index are derived．graphic applications Oil Fibonacci numbers are pictured．For Hosoya index．Counting theory of S 。。factors has interesting．value and substantial advance in its field．Hosova index for Chemistry is presented mathematical value by graph theory．

Key words: Graph theory, Fibonacci numbers, The number of—factors, Hosoya inde