Dual of a planar graph
Task number: 4069
Show that for a planar graph \( G \) and its dual \( G^* \) it holds that: \( T_G (x, y) = T_{G^*} (y, x) \).
Hint
Use the recurrent relation to calculate the Tutte polynomial.
Solution
Just note that the bridges in \( G \) correspond to the loops in \( G^* \) and that the loops in \( G \) correspond to the bridges in \( G^* \).
