Suppose that G is an Eulerian graph of order n 3 containing exactly three vertices of

Chapter 12, Problem 12

(choose chapter or problem)

Suppose that G is an Eulerian graph of order n 3 containing exactly three vertices of the same degree r and at most two vertices of any other degree. (a) Show that n is odd. (b) Show that n = 4k 1 or n = 4k + 1 for some positive integer k. (c) Show that if n = 4k 1 or n = 4k + 1, then r = 2k.

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