Abstract: Here a method enduing a matrix to each maximal outerplanar graph of order n is proposed to decide whether graphs are isomorphic,and it is proved that the matrix and the maximal outerplanar are one to one.After constructing all the possible maximal outerplanar graphs,the isomorphic ones are deleted and all the maximal outerplanar graphs are got.At the same time,the number of all the maximal outerplanar graphs of order n is obtained.This paper solves the problem how to decide whether graphs are isomorphic and how to compute all the maximal outerplanar graphs.

Key words: graph theory； maximal outerplanar graphs； isomorphic graph； Hamilton cycle；