An introduction to graph theory
Pirzada, S.
An introduction to graph theory S. Pirzada - Hyderabad: University Press, 2009. - viii, 396 p. ill.
Include references and index.
1. Introduction
1.1 Basic Concepts
1.2 Degrees
1.3 Isomorphism
1.4 Types of Graphs
1.5 Graph Properties
1.6 Paths, Cycles and Components
1.7 Operations on Graphs
1.8 Topological Operations
1.9 Distance and Eccentricity
1.10 Exercises
2. Degree Sequences
2.1 Degree Sequences
2.2 Criteria for Degree Sequences
2.3 Degree Set of a Graph
2.4 New Criterion
2.5 Equivalence of Seven Criteria
2.6 Signed Graphs
2.7 Exercises
3. Eulerian and Hamiltonian Graphs
3.1 Euler, Graphs
3.2 Konigsberg Bridge Problem
3.3 Unicursal Graphs
3.4 Arbitrarily Traceable Graphs
3.5 Sub-Eulerian Graphs
3.6 Hamiltonian Graphs
3.7 Pancyclic Graphs
3.8 Exercises
4. Trees
4.1 Basics
4.2 Rooted and Binary Trees
4.3 Number of Labelled Trees
4.4 The Fundamental Cycles
4.5 Generation of Trees
4.6 Helly Property
4.7 Signed Trees
4.8 Exercises
5. Connectivity
5.1 Basic Concepts
5.2 Block-Cut Vertex Tree
5.3 Connectivity Parameters
5.4 Menger's Theorem
5.5 Some Properties of a Bond
5.6 Fundamental Bonds
5.7 Block Graphs and Cut Vertex Graphs
5.8 Exercises
6. Planarity
6.1 Kuratowski's two graphs
6.2 Region
6.3 Euler's Theorem
6.4 Kuratowski's theorem
6.5 Geometric Dual
6.6 Polyhedron
6.7 Decomposition of Some Planar Graphs
6.8 Exercises
7. Colourings
7.1 Vertex Colouring
12 Critical Graphs
7.3 Brooks Theorem
7.4 Edge Colouring
7.5 Region Colouring (Map Coloring)
7.6 Heawood Map-Colouring Theorem
7.7 Uniquely Colourable Graphs
7.8 Hajos Conjecture
7.9 Exercises
8. Matchings and Factors
8.1 Matchings
8.2 Factors
8.3 Antifactor Sets
8.4 The /-factor Theorem
8.5 Degree Factors
8.6 (g, f) and [a, b]-factors
8.7 Exercises
9. Edge Graphs and Eccentricity Sequences
9.1 Edge Graphs
9.2 Edge Graphs and Traversability
9.3 Total Graphs
9.4 Eccentricity Sequences and Sets
9.5 Distance Degree Regular and Distance Regular Graphs
9.6 Isometry
9.7 Exercises
10. Graph Ma^trices
10.1 Incidence Matrix
10.2 Submatrices of A(G)
10.3 Cycle Matrix
10.4 Cut-Set Matrix
10.5 Fundamental Cut Set Matrix
10.6 Relations between A/, Bf and C/
10.7 Path Matrix
10.8 Adjacency Matrix
10.9 Exercises
11. Digraphs
11.1 Basic Definitions ,
11.2 Digraphs Mid Binary Relations .
11.3 Directed Paths and Connectedness
11.4 Buler Digraphs
11.5 Hamiltonian Digraphs
11.6 Trees with Directed Edges
11.7 Matrices A, B and C of Digraphs
11.8 Number of Arborescences
11.9 Tournaments
11.10 Exercises
12. Score Structure in Digraphs
12.1 Score Sequences in Tournaments
12.2 Frequency Sets in Tournaments
12.3 Score Sets in Tournaments
12.4 Lexicographic Enumeration and Tournament Construction
12.5 Simple Score Sequences in Tournaments
12.6 Score Sequences of Self-Converse Tournaments .
12.7 Score Sequences of Bipartite Tournaments
12.8 Uniquely Realisable (simple) Pairs of Score Sequences
12.9 Score Sequences of Oriented Graphs
12.10 Score Sets in Oriented Graphs
12.11 Uniquely Realisable (simple) Score Sequences in Oriented Graphs
12.12 Score Sequences in Oriented Bipartite Graphs
12.13 Score Sequences of Semi Complete Digraphs
12.14 Exercises
9788173717604
Isomorphism
Graph
006.6 / PIR/I
An introduction to graph theory S. Pirzada - Hyderabad: University Press, 2009. - viii, 396 p. ill.
Include references and index.
1. Introduction
1.1 Basic Concepts
1.2 Degrees
1.3 Isomorphism
1.4 Types of Graphs
1.5 Graph Properties
1.6 Paths, Cycles and Components
1.7 Operations on Graphs
1.8 Topological Operations
1.9 Distance and Eccentricity
1.10 Exercises
2. Degree Sequences
2.1 Degree Sequences
2.2 Criteria for Degree Sequences
2.3 Degree Set of a Graph
2.4 New Criterion
2.5 Equivalence of Seven Criteria
2.6 Signed Graphs
2.7 Exercises
3. Eulerian and Hamiltonian Graphs
3.1 Euler, Graphs
3.2 Konigsberg Bridge Problem
3.3 Unicursal Graphs
3.4 Arbitrarily Traceable Graphs
3.5 Sub-Eulerian Graphs
3.6 Hamiltonian Graphs
3.7 Pancyclic Graphs
3.8 Exercises
4. Trees
4.1 Basics
4.2 Rooted and Binary Trees
4.3 Number of Labelled Trees
4.4 The Fundamental Cycles
4.5 Generation of Trees
4.6 Helly Property
4.7 Signed Trees
4.8 Exercises
5. Connectivity
5.1 Basic Concepts
5.2 Block-Cut Vertex Tree
5.3 Connectivity Parameters
5.4 Menger's Theorem
5.5 Some Properties of a Bond
5.6 Fundamental Bonds
5.7 Block Graphs and Cut Vertex Graphs
5.8 Exercises
6. Planarity
6.1 Kuratowski's two graphs
6.2 Region
6.3 Euler's Theorem
6.4 Kuratowski's theorem
6.5 Geometric Dual
6.6 Polyhedron
6.7 Decomposition of Some Planar Graphs
6.8 Exercises
7. Colourings
7.1 Vertex Colouring
12 Critical Graphs
7.3 Brooks Theorem
7.4 Edge Colouring
7.5 Region Colouring (Map Coloring)
7.6 Heawood Map-Colouring Theorem
7.7 Uniquely Colourable Graphs
7.8 Hajos Conjecture
7.9 Exercises
8. Matchings and Factors
8.1 Matchings
8.2 Factors
8.3 Antifactor Sets
8.4 The /-factor Theorem
8.5 Degree Factors
8.6 (g, f) and [a, b]-factors
8.7 Exercises
9. Edge Graphs and Eccentricity Sequences
9.1 Edge Graphs
9.2 Edge Graphs and Traversability
9.3 Total Graphs
9.4 Eccentricity Sequences and Sets
9.5 Distance Degree Regular and Distance Regular Graphs
9.6 Isometry
9.7 Exercises
10. Graph Ma^trices
10.1 Incidence Matrix
10.2 Submatrices of A(G)
10.3 Cycle Matrix
10.4 Cut-Set Matrix
10.5 Fundamental Cut Set Matrix
10.6 Relations between A/, Bf and C/
10.7 Path Matrix
10.8 Adjacency Matrix
10.9 Exercises
11. Digraphs
11.1 Basic Definitions ,
11.2 Digraphs Mid Binary Relations .
11.3 Directed Paths and Connectedness
11.4 Buler Digraphs
11.5 Hamiltonian Digraphs
11.6 Trees with Directed Edges
11.7 Matrices A, B and C of Digraphs
11.8 Number of Arborescences
11.9 Tournaments
11.10 Exercises
12. Score Structure in Digraphs
12.1 Score Sequences in Tournaments
12.2 Frequency Sets in Tournaments
12.3 Score Sets in Tournaments
12.4 Lexicographic Enumeration and Tournament Construction
12.5 Simple Score Sequences in Tournaments
12.6 Score Sequences of Self-Converse Tournaments .
12.7 Score Sequences of Bipartite Tournaments
12.8 Uniquely Realisable (simple) Pairs of Score Sequences
12.9 Score Sequences of Oriented Graphs
12.10 Score Sets in Oriented Graphs
12.11 Uniquely Realisable (simple) Score Sequences in Oriented Graphs
12.12 Score Sequences in Oriented Bipartite Graphs
12.13 Score Sequences of Semi Complete Digraphs
12.14 Exercises
9788173717604
Isomorphism
Graph
006.6 / PIR/I