My graph theory book postulates the if a simple graph with n vertices has at least C(n - 1, 2) + 2 edges then the graph must be Hamiltonian.
This is probably true but I am confused by the notation of what C(n - 1, 2) means?
C usually represents a cycle but clearly not in this case. And whatever function they are referencing takes 2 parameters which is quite strange.
It is the binomial coefficient $n-1$ choose $2$, i.e. $$\binom{n-1}{2},$$ which is $$\frac{(n-1)(n-2)}{2}.$$ In general, $C(n,k)$ is alternative notation used for the binomial coefficient $\binom{n}{k}$, which is defined by $$\binom{n}{k} = \frac{n!}{k!(n-k)!}.$$