This comprehensive compendium discusses the basics of graph theory to its application, focusing on the application of graph theory to mobile communications. A mobile communication connects a mobile terminal and a base station wirelessly, and the base station enables communications all over the world via a wired and satellite communication system. This means that the mobile communication system includes wire and wireless technologies, and also hardware such as analog electric circuits, digital circuits and a software part such as computer algorithms. This useful reference text deeply studies how the network structure influences the performance of the corresponding system.
Author(s): Masakazu Sengoku
Series: ADVANCED SERIES IN ELECTRICAL AND COMPUTER ENGINEERING
Publisher: World Scientific Publishing Co
Year: 2023
Language: English
Pages: 409
Contents
Preface
About the Author
Acknowledgments
Chapter 1. Introduction
Bibliography
Chapter 2. Basic Concept of Graphs
2.1. Definitions
2.2. Special graphs
2.3. Subgraphs
2.4. Paths, Ties and Components
2.5. Graph Operations
2.6. Cuts
2.7. Tiesets and Cutsets
Bibliography
Chapter 3. Trees, Cotrees and Hybrid Trees
3.1. Trees
3.2. Cotrees
3.3. Fundamental Cutsets and Fundamental Tiesets
3.4. Short-Circuiting and Open-Circuiting
3.5. Hybrid Trees
3.5.1. Definition of hybrid trees
3.5.2. Number of edges of a hybrid tree
3.5.3. Hybrid Tree Graphs
Bibliography
Chapter 4. Matrix and Application of Trees
4.1. Matrices of Graphs
4.1.1. Adjacency matrix
4.1.2. Incidence matrix
4.1.3. Tieset matrix
4.1.4. Cutset matrix
4.2. Application to Linear Networks
4.3. Tellegen’s Theorem in Electrical Networks
4.4. Tree and Computer Algorithm
4.4.1. Binary tree and the amount of calculation
4.4.2. Königsberg bridge problem
4.4.3. Hamiltonian cycle problem
4.4.4. Shortest path problem
4.4.5. Maximum flow problem
4.4.6. Coloring problem
Bibliography
Chapter 5. Graphical Views of Electrical and Electronic Networks
5.1. Graphical Consideration of Electrical Networks Analysis
5.1.1. Some analysis methods
5.1.2. Graphical considerations by trees
5.1.3. Graphical considerations by the series and parallel
5.1.4. Graphical considerations by hybrid trees
5.1.5. A network with controlled source
5.2. Algebraic Considerations of Hybrid Trees and Hybrid k-Trees
5.2.1. Definitions and preliminary considerations
5.2.2. Hybrid trees and hybrid k-trees
5.2.3. Some properties of hybrid trees and hybrid k-trees
5.3. Sensitivity Analysis in Signal Flow Graphs
5.3.1. Tellegen’s theorem in signal flow graphs
5.3.2. Operators in signal flow graphs
5.3.3. Operators in signal flow graphs with nonisomorphic graphs
5.3.4. Applications of the SFG operators
5.3.5. Summary of the SFG operators
Bibliography
Chapter 6. Mobile Communication Systems (1)
6.1. Introduction for Mobile Communication Systems
6.2. Location Problems on Graphs and Networks
6.2.1. Minimum tree problem
6.2.2. Maximum tree problem
6.2.3. Center problems
6.2.3.1. Eccentricity of a vertex by shortest paths
6.2.3.2. Eccentricity of a vertex by maximum flows
6.2.3.3. Eccentricity of an edge by tiesets and cutsets
6.2.3.4. Meaning of application of the concept of center of graph
6.2.4. Median problems
6.2.4.1. Median problem by distance
6.2.4.2. Median problem by gauge
6.2.5. Generalizations of centrality in graphs and networks
6.2.5.1. The reduction of metric space
6.2.5.2. The centrality function in metric space
6.2.5.3. Characterizing a form of centrality function
6.2.5.4. Some centrality functions in a graph
6.2.5.5. Some other centrality functions in a graph
6.2.6. Fault diagnosis by measuring transmission numbers
6.2.6.1. Out-transmission number and in-transmission number and their generalizations
6.2.6.2. Assumptions and a Fault of an Edge
6.2.6.3. Increment of distance by increase of the length of an edge
6.2.6.4. Detection of a fault edge
Bibliography
Chapter 7. Mobile Communication Systems (2)
7.1. Cellular Systems and Graphs
7.1.1. Cellular systems in mobile communication systems
7.1.1.1. The cell structure
7.1.1.2. Channels and buffer cells in a cellular system
7.1.1.3. Coloring problems of graphs and channel assignment problems
7.1.1.4. Communication traffic characteristics in a cellular system
7.1.2. Generalized coloring problems in mobile communication systems
7.1.2.1. Channel offset systems in a cellular mobile system
7.1.2.2. Another new coloring problem
7.1.2.3. Mixture of previous coloring concepts
7.1.3. Rearrangement in a cellular mobile system
7.1.3.1. An explanation of rearrangement by an example
7.1.3.2. A simulation result for a rearrangement
7.1.3.3. Other trends regarding cellular systems
7.1.4. Spatial data and mobile communications
7.1.4.1. The role of mobile communication in SD/GIS
7.1.4.2. The application of SD/GIS to mobile communication
7.1.4.3. The mobile terminals traffic and communication traffic
7.1.4.4. Cell Structure and computational geometry
7.2. Multihop Systems and Graphs
7.2.1. Multihop wireless networks
7.2.1.1. Strong edge coloring
7.2.1.2. CIR-edge coloring
7.2.2. Some control problems in multihop networks
7.2.2.1. Network coding and multihop wireless networks
7.2.2.2. Two-node-disjoint path routing in multihop wireless networks
7.3. Delay Tolerant Networks and Graphs
7.3.1. Epidemic communications
7.3.2. Emergency communications
Bibliography
Index
