A Research On Related Properities Of Hybrid Benzenoid System Graph

In this paper,we study the planar graph of a class of benzenoid hydrocarbons which contains only regular hexagons and one pentagon.Here we suppose the pentagon is only on the left side of the polyhexes,for instance,fluorence、coimarone etc. We call them Hybrid system in the paper.At first,by using of BEC code of the polyhexes,we write a suitable algorithm and create a new BEC code which satisfies the condition of the Hybrid system and by which we enumerate all the case. Secondly, we use the adjacency matrix of polyhexes to get the corresponding adjacency matrix of combined system.At the same time,we get the relationship between vertices(n)、edges(m)、the number of the hexagons (h) and the inner vertex (ni),such as m=n+h、n4h+5-ni、m=5h+5-ni etc.We also get another relationship of the hexagons and the BEC code n=4h+5+∑BEC/2. At last we provide a conjecture of the relationship between the number of the Hydrogens N(H),BEC code and the inner vertex as follow:if h is even,then N(H)=∑(α-1)+1.if h is odd and has no inner vertices, then N(H)=∑(α-1)+1.if h is odd and the number of the inner vertices is larger than1,then N(H)=∑(α-1)＋1＋1,where a is the number of the BEC code that is larger and equal than2,N(H) is the number of hydrogen.