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Textbook of Graph Theory 2nd ed. 2012 [Minkštas viršelis]

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  • Formatas: Paperback / softback, 292 pages, aukštis x plotis: 235x155 mm, weight: 469 g, 204 Illustrations, black and white; XIII, 292 p. 204 illus., 1 Paperback / softback
  • Serija: Universitext
  • Išleidimo metai: 20-Sep-2012
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1461445280
  • ISBN-13: 9781461445289
Kitos knygos pagal šią temą:
Textbook of Graph Theory 2nd ed. 2012Didesnis paveikslėlis
  • Formatas: Paperback / softback, 292 pages, aukštis x plotis: 235x155 mm, weight: 469 g, 204 Illustrations, black and white; XIII, 292 p. 204 illus., 1 Paperback / softback
  • Serija: Universitext
  • Išleidimo metai: 20-Sep-2012
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 1461445280
  • ISBN-13: 9781461445289
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781461445289.html
Raktažodžiai:

Graph theory experienced a tremendous growth in the 20th century. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. This textbook provides a solid background in the basic topics of graph theory, and is intended for an advanced undergraduate or beginning graduate course in graph theory.

This second edition includes two new chapters: one on domination in graphs and the other on the spectral properties of graphs, the latter including a discussion on graph energy. The chapter on graph colorings has been enlarged, covering additional topics such as homomorphisms and colorings and the uniqueness of the Mycielskian up to isomorphism. This book also introduces several interesting topics such as Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's proof of Kuratowski's theorem on planar graphs, the proof of the nonhamiltonicity of the Tutte graph on 46 vertices, and a concrete application of triangulated graphs.



In its second edition, expanded with new chapters on domination in graphs and on the spectral properties of graphs, this book offers a solid background in the basics of graph theory. Introduces such topics as Dirac's theorem on k-connected graphs and more.

Recenzijos

From the reviews of the second edition:

This book demonstrates the breadth of graph theory by including several explicit applications of graph theory to other disciplines. This could be used as a textbook for a graduate or undergraduate course. The streamlined text would make this a good reference book for an undergraduate or non-mathematician who uses graph theory. The embedded exercises make it a useful reference for a teacher of a graph theory course or a course in which selected topics of graph theory may occur. (Suzanne Caulk, MAA Reviews, June, 2013)

The book goes from the basics to the frontiers of research in graph theory, with newly ideas emergent, in mathematics or computer science. Definitely the book is high recommended and is of much interest. It provides a solid background in the basic topics of graph theory, and is an excellent guide for graduate. I feel sure that it will be of great use to students, teachers and researchers. (Francisco José Cano Sevilla, The European Mathematical Society, April, 2013)

1 Basic Results
1(36)
1.1 Introduction
1(1)
1.2 Basic Concepts
1(7)
1.3 Subgraphs
8(2)
1.4 Degrees of Vertices
10(3)
1.5 Paths and Connectedness
13(5)
1.6 Automorphism of a Simple Graph
18(2)
1.7 Line Graphs
20(4)
1.8 Operations on Graphs
24(2)
1.9 Graph Products
26(5)
1.10 An Application to Chemistry
31(1)
1.11 Application to Social Psychology
31(3)
1.12 Miscellaneous Exercises
34(3)
Notes
35(2)
2 Directed Graphs
37(12)
2.1 Introduction
37(1)
2.2 Basic Concepts
37(2)
2.3 Tournaments
39(3)
2.4 k-Partite Tournaments
42(5)
2.5 Exercises
47(2)
Notes
47(2)
3 Connectivity
49(24)
3.1 Introduction
49(1)
3.2 Vertex Cuts and Edges Cuts
49(4)
3.3 Connectivity and Edge Connectivity
53(6)
3.4 Blocks
59(2)
3.5 Cyclical Edge Connectivity of a Graph
61(1)
3.6 Menger's Theorem
61(9)
3.7 Exercises
70(3)
Notes
71(2)
4 Trees
73(24)
4.1 Introduction
73(1)
4.2 Definition, Characterization, and Simple Properties
73(4)
4.3 Centers and Centroids
77(4)
4.4 Counting the Number of Spanning Trees
81(3)
4.5 Cayley's Formula
84(2)
4.6 Helly Property
86(1)
4.7 Applications
87(7)
4.7.1 The Connector Problem
87(1)
4.7.2 Kruskal's Algorithm
88(2)
4.7.3 Prim's Algorithm
90(2)
4.7.4 Shortest-Path Problems
92(1)
4.7.5 Dijkstra's Algorithm
92(2)
4.8 Exercises
94(3)
Notes
95(2)
5 Independent Sets and Matchings
97(20)
5.1 Introduction
97(1)
5.2 Vertex-Independent Sets and Vertex Coverings
97(2)
5.3 Edge-Independent Sets
99(1)
5.4 Matchings and Factors
100(4)
5.5 Matchings in Bipartite Graphs
104(8)
5.6 Perfect Matchings and the Tutte Matrix
112(5)
Notes
115(2)
6 Eulerian and Hamiltonian Graphs
117(26)
6.1 Introduction
117(1)
6.2 Eulerian Graphs
117(5)
6.3 Hamiltonian Graphs
122(8)
6.3.1 Hamilton's "Around the World" Game
122(8)
6.4 Pancyclic Graphs
130(3)
6.5 Hamilton Cycles in Line Graphs
133(5)
6.6 2-Factorable Graphs
138(2)
6.7 Exercises
140(3)
Notes
141(2)
7 Graph Colorings
143(32)
7.1 Introduction
143(1)
7.2 Vertex Colorings
143(4)
7.2.1 Applications of Graph Coloring
143(4)
7.3 Critical Graphs
147(6)
7.3.1 Brooks' Theorem
149(2)
7.3.2 Other Coloring Parameters
151(1)
7.3.3 b-Colorings
152(1)
7.4 Homomorphisms and Colorings
153(2)
7.4.1 Quotient Graphs
154(1)
7.5 Triangle-Free Graphs
155(4)
7.6 Edge Colorings of Graphs
159(8)
7.6.1 The Timetable Problem
159(3)
7.6.2 Vizing's Theorem
162(5)
7.7 Snarks
167(1)
7.8 Kirkman's Schoolgirl Problem
168(2)
7.9 Chromatic Polynomials
170(5)
Notes
173(2)
8 Planarity
175(32)
8.1 Introduction
175(1)
8.2 Planar and Nonplanar Graphs
175(5)
8.3 Euler Formula and Its Consequences
180(4)
8.4 K5 and K3.3 are Nonplanar Graphs
184(2)
8.5 Dual of a Plane Graph
186(3)
8.6 The Four-Color Theorem and the Heawood Five-Color Theorem
189(2)
8.7 Kuratowski's Theorem
191(8)
8.8 Hamiltonian Plane Graphs
199(1)
8.9 Tait Coloring
200(7)
Notes
205(2)
9 Triangulated Graphs
207(14)
9.1 Introduction
207(1)
9.2 Perfect Graphs
207(2)
9.3 Triangulated Graphs
209(2)
9.4 Interval Graphs
211(3)
9.5 Bipartite Graph B(G) of a Graph G
214(1)
9.6 Circular Arc Graphs
215(1)
9.7 Exercises
215(1)
9.8 Phasing of Traffic Lights at a Road Junction
216(5)
Notes
219(2)
10 Domination in Graphs
221(20)
10.1 Introduction
221(1)
10.2 Domination in Graphs
221(3)
10.3 Bounds for the Domination Number
224(1)
10.4 Bound for the Size m in Terms of Order n and Domination Number y (G)
224(3)
10.5 Independent Domination and Irredundance
227(2)
10.6 Exercises
229(1)
10.7 Vizing's Conjecture
229(5)
10.8 Decomposable Graphs
234(3)
10.9 Domination in Direct Products
237(4)
Notes
238(3)
11 Spectral Properties of Graphs
241(34)
11.1 Introduction
241(1)
11.2 The Spectrum of a Graph
241(2)
11.3 Spectrum of the Complete Graph Kn
243(1)
11.4 Spectrum of the Cycle Cn
243(1)
11.4.1 Coefficients of the Characteristic Polynomial
244(1)
11.5 The Spectra of Regular Graphs
244(5)
11.5.1 The Spectrum of the Complement of a Regular Graph
245(1)
11.5.2 Spectra of Line Graphs of Regular Graphs
246(3)
11.6 Spectrum of the Complete Bipartite Graph Kp,q
249(1)
11.7 The Determinant of the Adjacency Matrix of a Graph
250(1)
11.8 Spectra of Product Graphs
251(2)
11.9 Cayley Graphs
253(2)
11.9.1 Introduction
253(1)
11.9.2 Unitary Cayley Graphs
254(1)
11.9.3 Spectrum of the Cayley Graph Xn
255(1)
11.10 Strongly Regular Graphs
255(3)
11.11 Ramanujan Graphs
258(3)
11.11.1 Why Are Ramanujan Graphs Important?
259(2)
11.12 The Energy of a Graph
261(8)
11.12.1 Introduction
261(1)
11.12.2 Maximum Energy of k-Regular Graphs
262(4)
11.12.3 Hyperenergetic Graphs
266(1)
11.12.4 Energy of Cayley Graphs
267(2)
11.13 Energy of the Mycielskian of a Regular Graph
269(3)
11.13.1 An Application of Theorem 11.13.1
271(1)
11.14 Exercises
272(3)
Notes
273(2)
List of Symbols 275(4)
References 279(8)
Index 287
R. Balakrishnan is currently an Adjunct Professor of Mathematics at Bharathidasan University in India.