Introduction to Graph Theory by Richard J. Trudeau

Author:Richard J. Trudeau
Language: eng
Format: epub
ISBN: 9780486318660
Publisher: Dover Publications

Proof of Euler’s Formula

Theorem 8. If G is polygonal then v + f − e = 2.

Proof. The proof is by induction on f. Let S be the statement, “v + f — e = 2 holds for all polygonal graphs having f faces”. Then S is a statement about positive integers f, and we shall use the principle of mathematical induction to prove that S is true for all positive integers. This of course will mean that the theorem is true.

To begin, then. By the principle of mathematical induction we have to demonstrate two things, the first of which is that

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