A recursive backtracking algorithm is designed

which uses the algorithm optimization strategy combined with pruning and prejudging function. It achieves the graceful verification for any graphs within finite points. Using this algorithm

the gracefulness of all the simple connected graphs are verifying in 9 points

and the number of all the graceful and ungraceful graphs is obtained in this range. the results show that the vast majority of the graphs are graceful in this range. And according to the experimental data

the following conclusions are also shown: a definite lower bound of graph K

n

-m (a graph of complete graph minus

m

edges) is ungraceful; when

p

and

q

satisfy certain conditions

all of this kind of (

p

q

）graphs  (

p

is the number of vertex

and

q

is the number of edges) are graceful; when

q

(mod 4)={0

3}

and

q

≤［3.7

p

-9.3

almost all of this kind of (

p

q

) graphs are graceful. And further guess

when

p

>

9

the relevant conclusions are rational.