CombinatorialTheory in Networks

Preface
    Part I  Networks and Graphs
Chapter 1  Fundamentals of Networks and Graphs
  1.1  Graphs and Networks
  1.2  Basic Concepts and Notations
  1.3  Trees and Planar Graphs
  1.4  Transmission Delay and Diameter
  1.5  Fault Tolerance and Connectivity
  1.6  Embedding and Routings
  1.7  Basic Principles of Network Design
  Exercises
Chapter 2  Symmetry of Graphs or Networks
  2.1  Fundamentals on Groups
  2.2  Vertex-Transitive Graphs
  2.3  Edge-Transitive Graphs
  2.4  Atoms of Graphs
  2.5  Connectivity of Transitive Graphs
  Exercises
    Part II  Bssic Methods of Network Designs
Chapter 3  Line Graphical Methods
  3.1  Line Graphs and Basic Properties
  3.2  Basic Properties of Line Digraphs
  3.3  Iterated Line Graphs
  3.4  Connectivity of Line Graphs
  Exercises
Chapter 4  Cayley Methods
  4.1  Cayley Graphs
  4.2  Transitivity of Cayley Graphs
  4.3  Atoms and Connectivity of Cayley Graphs
  4.4  Vertex-Transitive Graphs with Prime Order
  Exercises
Chapter 5  Cartesian Product Methods
  5.1  Cartesian Product of Graphs
  5.2  Diameter and Connectivity
  5.3  Other Properties of Cartesian Products
  5.4  Generalized Cartesian Products
  Exercises
Chapter 6  Basic Problems in Optimal Designs
  6.1  Undirected (d,k)-Graph Problems
  6.2  Directed (d,k)-Graph Problems
  6.3  Relations between Diameter and Connectivity
  Exercises
    Part III  Well-Known Topologies of Networks
Chapter 7  Hypercube Networks
  7.1  Definitions and Basic Properties
  7.2  Gray Codes and Cycles
  7.3  Lengths of Paths
  7.4  Embedding Problems
  7.5  Generalized Hypercubes
  7.6  Some Variations of Hypercubes
  Exercises
Chapter 8  De Bruijn Networks
  8.1  Definitions and Basic Properties
  8.2  Uniqueness of Shortest Paths
  8.3  Generalized de Bruijn Digraphs
  8.4  Comparison with Hypercubes
  Exercises
Chapter 9  Kautz Networks
  9.1  Definitions and Basic Properties
  9.2  Generalized Kautz Digraphs
  9.3  Connectivity of Generalized Kautz Digraphs
  Exercises
Chapter 10  Double Loop Networks
  10.1  Double Loop Networks
  10.2  L-Tiles in the Plane
  10.3  L-Tiles and Double Loop Networks
  10.4  Design of Optimal Double Loop Networks
  10.5  Basic Properties of Circulant Networks
  Exercises
Chapter 11  Topologies of Other Networks
  11.1  Mesh Networks and Grid Networks
  11.2  Pyramid Networks
  11.3  Cube-Connected Cycles
  11.4  Butterfly Networks
  11.5  Benes Networks
  11.6  Networks
  11.7  Shuffle-Exchange Networks
  Exercises
    Part IV  Fault-Tolerant Analysis of Networks
Chapter 12  Routings in Networks
  12.1  Forwarding Index of Routing
  12.2  Edge-Forwarding Index of Routing
  12.3  Forwarding Indices of Some Graphs
  12.4 Delay of Fault-Tolerant Routing
  Exercises
Chapter 13  Fault-Tolerant Diameters in Networks
  13.1  Diameters of Altered Graphs
  13.2  Edge Fault-Tolerant Diameters
  13.3  Relations between Two Diameters
  13.4  Vertex Fault-Tolerant Diameters
  13.5  Fault-Tolerant Diameter of Product Graphs
  13.6  Fault-Tolerant Diameters of Some Networks
  Exercises
Chapter 14  Menger-Type Problems in Parallel Systems
  14.1  Menger-Type Problems
  14.2  Bounded Menger Number and Connectivity
  14.3  Bounded Edge-Connectivity
  14.4  Rabin Numbers of Networks
  Exercises
Chapter 15  Wide-Diameters of Networks
  15.1  Wide-Diameter and Basic Results
  15.2  Wide-Diameter of Regular Graphs
  15.3  Wide-Diameter of Cartesian Products
  15.4  Wide-Diameter and Independence Number
  15.5  Wide-Diameter and Fault-Tolerant Diameter
  15.6  Wide-Diameters of Some Networks
  Exercises
Chapter 16  Generalized Independence and Domination Numbers
  16.1  Generalized Independence Numbers
  16.2  Generalized Domination Numbers
  16.3  Distance Independence and Domination
  Exercises
Chapter 17  Restricted Fault-Tolerance of Networks
  17.1  Restricted Connectivity and Diameter
  17.2  Restricted Edge-Connectivity
  17.3  Restricted Edge-Atoms
  17.4  Results on Transitive Graphs
  17.5  Super Connectivity of Networks
  17.6  Super Edge-Connectivity of Networks
  17.7  Super Connectivity of Line Graphs
  17.8  Connectivity Restricted by Degree-Conditions
  17.9  Connectivity Restricted by Order-Conditions
  17.10  Restricted Connectivity of Some Networks
  Exercises
Bibliography
A List of Notations
Index