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 \( G^* \).

Difficulty level: Easy task (using definitions and simple reasoning)
Reasoning task
Cs translation
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