Download e-book for kindle: A Textbook of Graph Theory (2nd Edition) (Universitext) by R. Balakrishnan, K. Ranganathan

By R. Balakrishnan, K. Ranganathan

ISBN-10: 1461445299

ISBN-13: 9781461445296

Graph thought skilled a massive progress within the twentieth century. one of many major purposes for this phenomenon is the applicability of graph idea in different disciplines similar to physics, chemistry, psychology, sociology, and theoretical machine technological know-how. This textbook presents an excellent heritage within the simple subject matters of graph idea, and is meant for a complicated undergraduate or starting graduate path in graph theory.

This moment variation comprises new chapters: one on domination in graphs and the opposite at the spectral homes of graphs, the latter together with a dialogue on graph power. The bankruptcy on graph hues has been enlarged, overlaying extra themes resembling homomorphisms and shades and the distinctiveness of the Mycielskian as much as isomorphism. This publication additionally introduces numerous attention-grabbing issues corresponding to Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem at the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's evidence of Kuratowski's theorem on planar graphs, the facts of the nonhamiltonicity of the Tutte graph on forty six vertices, and a concrete program of triangulated graphs.

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Extra info for A Textbook of Graph Theory (2nd Edition) (Universitext)

Example text

2 Use induction to make the previous argument precise, and prove that n! > 2n if n ≥ 4. There is a formula that gives a very good approximation of n!. We state it without proof, since the proof (although not terribly difficult) needs calculus. 1 [Stirling’s formula] n n√ 2πn. 14 . . 718 . . is the base of the natural logarithm, and ∼ means approximate equality in the precise sense that n! ∼ n! √ n n e 2πn →1 (n → ∞). 32 2. Combinatorial Tools Both of the funny irrational numbers e and π occur in the same formula!

Have? We know by Stirling’s formula that √ 100! ≈ (100/e)100 · 200π. The number of digits of this number is its logarithm, in base 10, rounded up. 969 . . So the number of digits in 100! is about 158 (this is, in fact, the right value). 3 Inclusion-Exclusion In a class of 40, many students are collecting the pictures of their favorite rock stars. Eighteen students have a picture of the Beatles, 16 students have a picture of the Rolling Stones and 12 students have a picture of Elvis Presley (this happened a long time ago, when we were young).

The table is a bit silly (but with reason). First, we give a bonus of 1 to every student. Second, we record in a separate column whether the student is collecting (say) both the Beatles and Elvis Presley (the column labeled BE), even though this could be read off from the previous columns. Third, we put a −1 in columns recording the collecting of an odd number of pictures, and a 1 in columns recording the collecting of an even number of pictures. We compute the total sum of entries in this table in two different ways.

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A Textbook of Graph Theory (2nd Edition) (Universitext) by R. Balakrishnan, K. Ranganathan

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