Hence, G is connected.

Proving two graphs are not isomorphic requires finding an invariant (degree sequence, cycle length, etc.). The manual gives a checklist of invariants to test, which students rarely compile on their own.

Without a solution manual, a student stuck on problem 27 in Chapter 5 might spin their wheels for hours, unable to see the logical pivot required. Consequently, the search for spikes every October and March during midterm seasons.

This contradicts the fact that G has more than (n-1)(n-2)/2 edges.