Theory and Application of Graphs
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Chapter
1
Basic Concepts of Graphs
1.1
Graphs
and Graphical
Presentation
1.2
Graph
Isomorphism
1.3
Vertex
Degrees
1.4
Subgraphs
and Operations
1.5
Walks,
Paths
and Connection
1.6
Distances
and Diameters
1.7
Circuits
and Cycles
1.8
Eulerian
Graphs
1.9
Hamiltonian
Graphs
1.10
Matrix
Presentation
of Graphs
Applications
1.11
Primitive
Exponents of Primitive Matrices
Chapter
2
Trees and Graphic Spaces
2.1
Trees
and Spanning
Trees
2.2 Vector
Spaces of Graphs
2.3 The
Number of Spanning Trees
Applications
2.4 The
Minimum Connector Problem
2.5
The
Shortest Path Problem
2.6
The
Electrical Network Equations
Chapter
3
Plane Graphs and Planar Graphs
3.1
Plane Graphs and Euler¨s Formula
3.2
Kuratowski¨s Theorem
3.3
Dual
Graphs
Applications
3.4
Regular
Polyhedra
3.5
Layout
of
Printed Circuits
Chapter
4
Flows
and Connectivity
4.1
Network
Flows
4.2
Menger¨s
Theorem
4.3
Connectivity
Applications
4.4
Design
of Transportation Schemes
4.5
Design
of Optimal Transportation Schemes
4.6
The
Chinese Postman Problem
4.7
Construction
of Squared Rectangles
Chapter
5
Matchings and Independent Sets
5.1
Matchings
5.2
Independent
Sets
Applications
5.3
The
Personnel Assignment Problem
5.4
The
Optimal Assignment Problem
5.5
The
Traveling Salesman Problem
Chapter
6
Coloring Theory
6.1
Vertex
Colorings
6.2
Edge
Colorings
Applications
6.3
The
Four-Color Problem
Chapter
7
Graphs and Groups
7.1
Group
Presentation of Graphs
7.2
Transitive
Graphs
7.3
Graphic Presentation of Groups
Applications
7.4
Design
of Interconnection
Networks
Bibilography
List
of Symbols
Index
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