| Preface |
|
v | |
| About the Author |
|
ix | |
| Acknowledgments |
|
xi | |
|
|
|
1 | (6) |
|
|
|
5 | (2) |
|
Chapter 2 Basic Concept of Graphs |
|
|
7 | (24) |
|
|
|
7 | (4) |
|
|
|
11 | (1) |
|
|
|
12 | (2) |
|
2.4 Paths, Ties and Components |
|
|
14 | (2) |
|
|
|
16 | (4) |
|
|
|
20 | (3) |
|
|
|
23 | (8) |
|
|
|
30 | (1) |
|
Chapter 3 Trees, Cotrees and Hybrid Trees |
|
|
31 | (38) |
|
|
|
31 | (5) |
|
|
|
36 | (2) |
|
3.3 Fundamental Cutsets and Fundamental Tiesets |
|
|
38 | (3) |
|
3.4 Short-Circuiting and Open-Circuiting |
|
|
41 | (9) |
|
|
|
50 | (19) |
|
3.5.1 Definition of hybrid trees |
|
|
50 | (3) |
|
3.5.2 Number of edges of a hybrid tree |
|
|
53 | (9) |
|
|
|
62 | (5) |
|
|
|
67 | (2) |
|
Chapter 4 Matrix and Application of Trees |
|
|
69 | (50) |
|
|
|
69 | (14) |
|
|
|
69 | (3) |
|
|
|
72 | (2) |
|
|
|
74 | (5) |
|
|
|
79 | (4) |
|
4.2 Application to Linear Networks |
|
|
83 | (11) |
|
4.3 Tellegen's Theorem in Electrical Networks |
|
|
94 | (5) |
|
4.4 Tree and Computer Algorithm |
|
|
99 | (20) |
|
4.4.1 Binary tree and the amount of calculation |
|
|
99 | (7) |
|
4.4.2 Konigsberg bridge problem |
|
|
106 | (3) |
|
4.4.3 Hamiltonian cycle problem |
|
|
109 | (1) |
|
4.4.4 Shortest path problem |
|
|
110 | (1) |
|
4.4.5 Maximum flow problem |
|
|
111 | (2) |
|
|
|
113 | (3) |
|
|
|
116 | (3) |
|
Chapter 5 Graphical Views of Electrical and Electronic Networks |
|
|
119 | (82) |
|
5.1 Graphical Consideration of Electrical Networks Analysis |
|
|
119 | (34) |
|
5.1.1 Some analysis methods |
|
|
119 | (5) |
|
5.1.2 Graphical considerations by trees |
|
|
124 | (8) |
|
5.1.3 Graphical considerations by the series and parallel |
|
|
132 | (3) |
|
5.1.4 Graphical considerations by hybrid trees |
|
|
135 | (7) |
|
5.1.5 A network with controlled source |
|
|
142 | (11) |
|
5.2 Algebraic Considerations of Hybrid Trees and Hybrids-Trees |
|
|
153 | (16) |
|
5.2.1 Definitions and preliminary considerations |
|
|
153 | (2) |
|
5.2.2 Hybrid trees and hybrid k-trees |
|
|
155 | (2) |
|
5.2.3 Some properties of hybrid trees and hybrid k-trees |
|
|
157 | (12) |
|
5.3 Sensitivity Analysis in Signal Flow Graphs |
|
|
169 | (32) |
|
5.3.1 Tellegen's theorem in signal flow graphs |
|
|
170 | (4) |
|
5.3.2 Operators in signal flow graphs |
|
|
174 | (7) |
|
5.3.3 Operators in signal flow graphs with nonisomorphic graphs |
|
|
181 | (4) |
|
5.3.4 Applications of the SFG operators |
|
|
185 | (13) |
|
5.3.5 Summary of the SFG operators |
|
|
198 | (1) |
|
|
|
199 | (2) |
|
Chapter 6 Mobile Communication Systems (1) |
|
|
201 | (92) |
|
6.1 Introduction for Mobile Communication Systems |
|
|
201 | (4) |
|
6.2 Location Problems on Graphs and Networks |
|
|
205 | (88) |
|
6.2.1 Minimum tree problem |
|
|
206 | (7) |
|
6.2.2 Maximum tree problem |
|
|
213 | (5) |
|
|
|
218 | (19) |
|
|
|
237 | (5) |
|
6.2.5 Generalizations of centrality in graphs and networks |
|
|
242 | (28) |
|
6.2.6 Fault diagnosis by measuring transmission numbers |
|
|
270 | (19) |
|
|
|
289 | (4) |
|
Chapter 7 Mobile Communication Systems (2) |
|
|
293 | (92) |
|
7.1 Cellular Systems and Graphs |
|
|
293 | (67) |
|
7.1.1 Cellular systems in mobile communication systems |
|
|
293 | (28) |
|
7.1.2 Generalized coloring problems in mobile communication systems |
|
|
321 | (20) |
|
7.1.3 Rearrangement in a cellular mobile system |
|
|
341 | (8) |
|
7.1.4 Spatial data and mobile communications |
|
|
349 | (11) |
|
7.2 Multihop Systems and Graphs |
|
|
360 | (15) |
|
7.2.1 Multihop wireless networks |
|
|
360 | (12) |
|
7.2.2 Some control problems in multihop networks |
|
|
372 | (3) |
|
7.3 Delay Tolerant Networks and Graphs |
|
|
375 | (10) |
|
7.3.1 Epidemic communications |
|
|
375 | (3) |
|
7.3.2 Emergency communications |
|
|
378 | (1) |
|
|
|
378 | (7) |
| Index |
|
385 | |
