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(Solved): 4. In a planar graph, \( s \) faces have degree 4 and \( t \) faces have degree 3. Both \( s \) an ...
4. In a planar graph, \( s \) faces have degree 4 and \( t \) faces have degree 3. Both \( s \) and \( t \) are positive integers. We also know that all vertices have degree 3. Using the Handshake Lemma, Euler's formula, and the idea of the previous exercise, show that the graph has exactly 5 faces (solve for \( s \) and t).
Expert Answer
Solution: Given The Handshake Lemma states that the sum of the degrees of all the vertices in a graph is equal to twice the number of edges. In a plan