Graph theory Q1 (basic)
Let be a -regular connected graph with 24 edges. Let be the number of vertices of .
Find is the sum of all possible value of .
The answer is 60.
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1 solution
From hand-shaking Lemma, k n = 2 ( 2 4 ) = 4 8 and 1 < k ≤ n − 1 as G is a connected graph. The possible values of ( k , n ) = ( 2 , 2 4 ) , ( 3 , 1 6 ) , ( 4 , 1 2 ) , ( 6 , 8 ) . Then the answer is 2 4 + 1 6 + 1 2 + 8 = 6 0 .