Flows and Connectivity · Flow Polynomial (Optional)

Lesson 9

Nikolai Chukhin · Alexander S. Kulikov

Problem. Find the flow polynomial of the graph below.

Hint:
Orient all three edges in the same direction. Conservation forces the three values \(\phi_{1},\phi_{2},\phi_{3}\in\Gamma\) to sum to \(0\). How many ordered triples of nonzero elements of a group of size \(q\) satisfy \(\phi_{1}+\phi_{2}+\phi_{3}=0\)?

1 point