A Textbook of Graph Theory

by R. Balakrishnan

Here is a solid introduction to graph theory, covering Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, Fournier's proof of Kuratowski's theorem on planar graphs, and more. The book does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics.

Genres: Mathematics

238 pages, Hardcover

First published December 17, 1999

About the author

R. Balakrishnan (ஆர். பாலகிருஷ்ணன்), a postgraduate in Tamil literature, is the first student of Tamil literature to clear the Civil Service exam. He joined the Indian Administration Service in 1984. His initial postings in the Tribal areas of Odisha triggered his interest in Indology, Anthropology and Place-name Studies. It was Iravatham Mahadevan who led Balakrishnan into the area of Indus Studies.

Balakrishnan has published several research papers on Place-name Studies, Odisha's history, and it's plural culture. Using Geographical Information System tools, he formulated the 'Korkai-Vanji-Tondi Complex', a place-name complex in the Indus geography. His paper on High-West:Low-East Dichotomy of Indus cities gained wide attention. His Tamil books on the Dravidian foundations of Indus Civilization received accolades as the 'best book written in Tamil on the subject'.

Balakrishnan is an author, poet and has published several books in Tamil. After 34 years of service with the Government of Odisha and the Government of India, he retired from the Civil Services in 2018. He is currently the Honorary Consultant of the Indus Research Centre of the Roja Muthaih Research Library, Chennai.

Reviews

[Justpassingby]

I started to read this book in order to fill a gap in my education. I was trained as a mathematician a long time ago, but somehow always managed to avoid courses on graph theory.

I was rewarded with a breadth-first presentation of this rich subject. The authors take care to guide us from elementary concepts to some of the more recent advanced results. This comes at the cost of continuity: many chapters represent a somewhat unnatural break from the preceding ones. In some cases there is even a repetition of the same definition in different terms, e.g., the definition of the different types of graph product in chapter 1 appears somewhat disconnected from the concept of a non-complete extended P-sum in chapter 11 even though they represent the same underlying idea.

For a second edition this book appears sloppily edited, if at all. I know that Springer tries to cut costs, but surely the authors could have gathered some feedback from early readers to eliminate many of the time-wasting typos in mathematical expressions?

Most chapters offer a useful review in the form of perfectly doable exercises.