A near Goldbach graph is a simple undirected graph whose vertex set consists of all positive even integers and there is an edge between two vertices a,b if and only if 2a+b,2∣a−b∣
Nearby in the stack
are either odd primes or
1
. A finite near Goldbach graph
G(n)
has the vertex set
{x∈2N:x≤2n}
with the same adjacency rule. In this paper, we obtain two exact formulas for the degree of the even positive integer
x
in
G(x/2)
. We compute a function
η(x)=p∣x,p>2∏p−2p−1(logx)2xe−0.183407
that approximates the degree of
x
in
G(x/2)
for a large even positive integer
x
. Finally, we introduce the concept of a nearly independent set of events and show that if the set of divisibility events for a large even integer