Graph Theory pp 1-25 | Cite as

# Fundamentals

Chapter

## Abstract

The purpose of this introduction is to familiarise the reader with the basic concepts and results of graph theory. The chapter inevitably contains a large number of definitions and in order to prevent the reader growing weary we prove simple results as soon as possible. The reader is not expected to have complete mastery of Chapter I before sampling the rest of the book, indeed, he is encouraged to skip ahead since most of the terminology is self-explanatory. We should add at this stage that the terminology of graph theory is far from being standard, though that used in this book is well accepted.

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### Notes

- Theorem 14 is in K. Kuratowski, Sur le problème des courbes gauches en topologie,
*Fund. Math.***15**(1930) 271–283MATHGoogle Scholar - for a simpler proof see G. A. Dirac and S. Schuster, A theorem of Kuratowski,
*Indag. Math.***16**(1954) 343–348.MathSciNetGoogle Scholar - The theorem of S. A. Amitsur and J. Levitzki (Theorem 14) is in Minimal identities for algebras,
*Proc. Amer. Math. Soc.***1**(1950) 449–463MathSciNetMATHCrossRefGoogle Scholar - the proof given in the text is based on R. G. Swan, An application of graph theory to algebra,
*Proc. Amer. Math. Soc.***14**(1963) 367–373.MathSciNetMATHCrossRefGoogle Scholar - R. G. Swan, Correction to “An application of graph theory to algebra,”
*Proc. Amer. Math. Soc.***21**(1969) 379–380.MathSciNetGoogle Scholar

## Copyright information

© Springer-Verlag New York Inc. 1979