# On an Inequality Arising in a Comparison of Hypercubes and Star Graphs

# Gideon Ehrlich and Jeremy Schiff

We define an *enkay pair* to be a
pair of positive integers (n,k) such that (n-1)(n-1)! < 2^{k} < n! .
This inequality arises when comparing a hypercube with
the smallest larger star graph. We list the 15 enkay pairs with
n ≤ 10^{6}, and speculate on whether the number of enkay pairs
is finite or infinite.