et G be a finite group of order n and S be a subset of G not containing the idelltityelement of G. Let p (0<p<1) be a fixed number. We define the set of all labelled Cayley digraphs X(G,S) (S≤G\{1}) of G as a s...et G be a finite group of order n and S be a subset of G not containing the idelltityelement of G. Let p (0<p<1) be a fixed number. We define the set of all labelled Cayley digraphs 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∈C\{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.展开更多
文摘et G be a finite group of order n and S be a subset of G not containing the idelltityelement of G. Let p (0<p<1) be a fixed number. We define the set of all labelled Cayley digraphs 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∈C\{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.
