A recursive backtracking algorithm is designed by combining pruning with pre-judgment function. All the bicyclic graphs in 16 points are elegantly verified

and all elegant and non-elegant graphs in 16 points are obtained. According to the experimental results

when 4≤p≤16 and

p

+1=1(mod 4)

the bicyclic graphs

C

(m

n)

is a non-elegant graph

and the number of non-elegant graphs are p/2－2

and all the other bicyclic graphs are elegant graphs. Finally

the conjecture is given: the bicyclic graphs are almost all elegant graphs.