Final answer:
Using graph theory concepts, the average degree of a tree with n vertices is 2(n-1)/n. Given the average degree of 1.9992, solving the equation mathematically shows that the number of vertices n in the tree graph is approximately 1000.
Step-by-step explanation:
The question asked revolves around a mathematical concept relating to graph theory, specifically in regards to a tree graph. A tree is a connected graph with no cycles and in a tree with n vertices, it follows that there are exactly n-1 edges. The degree of a vertex is the number of edges connected to it, and in a tree, the sum of the degrees of all vertices is twice the number of edges.
Therefore, for a tree with n vertices, the sum of all degrees is 2(n-1). When the average degree is given as 1.9992, we use the formula for the average degree of a tree, which is 2(n-1)/n, to obtain 1.9992 and solve for n. The equation is:
1.9992 = 2(n-1)/n
After solving this equation, we can determine that the number of vertices n must be very close to 1000 because the average degree of 1.9992 is almost 2, meaning a tiny fraction is subtracted from 2 when dividing by n. Since the fraction taken from the average degree is very small, the number of vertices must be very large. More formally, by cross-multiplying and solving for n, we will find n is indeed 1000.