Graph theory / Frank Harary.
Series Addison-Wesley series in mathematicsEditor: Reading, Mass. : Addison-Wesley, c1969Descripción: ix, 274 p. : il. ; 24 cmTema(s): Graph theoryOtra clasificación: 05CxxCONTENTS I hate quotations. Tell me what you know. R. W. Emerson 1 Discovery . [1] The Konigsberg bridge problem [1] Electric networks [2] Chemical isomers [3] Around the world [4] The Four Color Conjecture [5] Graph theory in the 20th century [5] 2 Graphs [8] Varieties of graphs [8] Walks and connectedness [13] Degrees [14] The problem of Ramsey [15] Extremal graphs [17] Intersection graphs [19] Operations on graphs [21] 3 Blocks [26] Cutpoints, bridges, and blocks [26] Block graphs and cutpoint graphs [29] 4 Trees [32] Characterization of trees [32] Centers and centroids [35] Block-cutpoint trees [36] Independent cycles and cocycles [37] Matroids [40] 5 Connectivity [43] Connectivity and line-connectivity [43] Graphical variations of Menger’s theorem [47] Further variations of Menger’s theorem [52] 6 Partitions [57] 7 Traversability [64] Eulerian graphs [64] Hamiltonian graphs [65] 8 Line Graphs [71] Some properties of line graphs [71] Characterizations of line graphs [73] Special line graphs [77] Line graphs and traversability [79] Total graphs [82] 9 Factorization [84] 1- factorization [84] 2- factorization [88] Arboricity [90] 10 Coverings [94] Coverings and independence [94] Critical points and lines [97] Line-core and point-core [98] 11 Planarity [102] Plane and planar graphs [102] Outerplanar graphs [106] Kuratowski’s theorem [108] Other characterizations of planar graphs [113] Genus, thickness, coarseness, crossing number [116] 12 Colorability [126] The chromatic number [126] The Five Color Theorem [130] The Four Color Conjecture [131] The Heawood map-coloring theorem [135] Uniquely colorable graphs [137] Critical graphs [141] Homomorphisms [143] The chromatic polynomial [145] 13 Matrices [150] The adjacency matrix [150] The incidence matrix [152] The cycle matrix [154] 14 Groups [160] The automorphism group of a graph [160] Operations on permutation groups [163] The group of a composite graph [165] Graphs with a given group [168] Symmetric graphs [171] Highly symmetric graphs [173] 15 Enumeration [178] Labeled graphs [178] Polya’s enumeration theorem [180] Enumeration of graphs [185] Enumeration of trees [187] Power group enumeration theorem [191] Solved and unsolved graphical enumeration problems [192] 16 Digraphs [198] Digraphs and connectedness [198] Directional duality and acyclic digraphs [200] Digraphs and matrices [202] Tournaments [205] Appendix I Graph Diagrams [213] Appendix II Digraph Diagrams [225] Appendix III Tree Diagrams [231] Bibliography [237] Index of Symbols [269] Index of Definitions [273]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 05 H254g (Browse shelf) | Available | A-5178 |
Bibliografía: p. 237-262.
CONTENTS --
I hate quotations. Tell me what you know. R. W. Emerson --
1 Discovery . [1] --
The Konigsberg bridge problem [1] --
Electric networks [2] --
Chemical isomers [3] --
Around the world [4] --
The Four Color Conjecture [5] --
Graph theory in the 20th century [5] --
2 Graphs [8] --
Varieties of graphs [8] --
Walks and connectedness [13] --
Degrees [14] --
The problem of Ramsey [15] --
Extremal graphs [17] --
Intersection graphs [19] --
Operations on graphs [21] --
3 Blocks [26] --
Cutpoints, bridges, and blocks [26] --
Block graphs and cutpoint graphs [29] --
4 Trees [32] --
Characterization of trees [32] --
Centers and centroids [35] --
Block-cutpoint trees [36] --
Independent cycles and cocycles [37] --
Matroids [40] --
5 Connectivity [43] --
Connectivity and line-connectivity [43] --
Graphical variations of Menger’s theorem [47] --
Further variations of Menger’s theorem [52] --
6 Partitions [57] --
7 Traversability [64] --
Eulerian graphs [64] --
Hamiltonian graphs [65] --
8 Line Graphs [71] --
Some properties of line graphs [71] --
Characterizations of line graphs [73] --
Special line graphs [77] --
Line graphs and traversability [79] --
Total graphs [82] --
9 Factorization [84] --
1- factorization [84] --
2- factorization [88] --
Arboricity [90] --
10 Coverings [94] --
Coverings and independence [94] --
Critical points and lines [97] --
Line-core and point-core [98] --
11 Planarity [102] --
Plane and planar graphs [102] --
Outerplanar graphs [106] --
Kuratowski’s theorem [108] --
Other characterizations of planar graphs [113] --
Genus, thickness, coarseness, crossing number [116] --
12 Colorability [126] --
The chromatic number [126] --
The Five Color Theorem [130] --
The Four Color Conjecture [131] --
The Heawood map-coloring theorem [135] --
Uniquely colorable graphs [137] --
Critical graphs [141] --
Homomorphisms [143] --
The chromatic polynomial [145] --
13 Matrices [150] --
The adjacency matrix [150] --
The incidence matrix [152] --
The cycle matrix [154] --
14 Groups [160] --
The automorphism group of a graph [160] --
Operations on permutation groups [163] --
The group of a composite graph [165] --
Graphs with a given group [168] --
Symmetric graphs [171] --
Highly symmetric graphs [173] --
15 Enumeration [178] --
Labeled graphs [178] --
Polya’s enumeration theorem [180] --
Enumeration of graphs [185] --
Enumeration of trees [187] --
Power group enumeration theorem [191] --
Solved and unsolved graphical enumeration problems [192] --
16 Digraphs [198] --
Digraphs and connectedness [198] --
Directional duality and acyclic digraphs [200] --
Digraphs and matrices [202] --
Tournaments [205] --
Appendix I Graph Diagrams [213] --
Appendix II Digraph Diagrams [225] --
Appendix III Tree Diagrams [231] --
Bibliography [237] --
Index of Symbols [269] --
Index of Definitions [273] --
MR, 41 #1566
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