Let
G be a finite group of order
n and
S be a subset of
G not containing the identity element of
G. Let
p (0
p<1) be="" a="" fixed="" number.="" we="" define="" the="" set="" of="" all="" labelled="" cayley="">
X(
G,
S) (
S<>
G\{1}) of
G as a sample space and assign a probability measure by requiring
P(
a
S)=
p for any
a
G\{1}. Here it is shown that the probability of the set of Cayley digraphs of
G with diameter 2 approaches 1 as the order
n of
G approaches infinity.
Key words Random Cayley digraph
This work is supported by the National Natural Science Foundation of China.