نمودارهای خطی و شبکه‌های الکتریکی

Title page......Page 1 Preface......Page 5 Contents......Page 7 1-1 Survey of applications......Page 9 1-2 The nonoriented graph......Page 16 Problems......Page 25 2-1 The Königsberger bridge problem......Page 27 2-2 Circuits......Page 30 2-3 Trees and fundamental systems of circuits......Page 32 2-4 Cut-sets and fundamental systems of cut-sets......Page 36 2-5 Cut-sets and circuits......Page 40 Problems......Page 41 3-1 Nonseparable graphs......Page 43 3-2 Planar graphs......Page 47 3-3 Dual graphs......Page 49 3-4 One terminal-pair graphs......Page 59 Problems......Page 61 4-1 The field modulo......Page 63 4-2 The vertex or incidence matrix......Page 69 4-3 The circuit matrix......Page 72 4-4 Nonsingular submatrices of A and B and formula for B_I......Page 76 4-5 The cut-set matrix......Page 80 4-6 Linear vector spaces......Page 84 4-7 Vector spaces associated with a graph......Page 91 Problems......Page 94 5-1 The vertex matrix......Page 96 5-2 The circuit matrix......Page 98 5-3 Nonsingular submatrices of A and B and formula for B_I......Page 100 5-4 Cut-sets of directed graphs......Page 103 5-5 Existence of graphs for given matrices......Page 106 5-6 Summary of important results on graphs......Page 119 Problems......Page 122 6-1 Kirchhoff's laws......Page 125 6-2 Mesh (loop) and node transformations......Page 130 6-3 The third postulate......Page 135 6-4 Loop and node systems of equations......Page 140 6-5 Energy functions and stability......Page 152 6-6 Dual networks......Page 157 Problems......Page 161 7-1 Node determinant and cofactors......Page 163 7-2 Driving-point and transfer admittances......Page 173 7-3 The short-circuit admittance functions......Page 176 7-4 Kirchhoff's rules......Page 179 7-5 General linear networks......Page 186 Problems......Page 202 8-1 Enumeration of natural frequencies......Page 205 8-2 One terminal-pair networks......Page 208 8-3 Two terminal-pair networks......Page 216 Problems......Page 234 9-1 Contact networks......Page 235 9-2 Sequential machines......Page 258 9-3 Logic networks......Page 268 Problems......Page 273 10-1 Communication networks......Page 276 10-2 Flow graphs and signal-flow graphs......Page 281 10-3 Calculus of binary relations......Page 294 10-4 Logic: axiomatics......Page 295 10-5 Brief survey of other applications......Page 297 Problems......Page 299 RESEARCH PROBLEMS......Page 303 BIBLIOGRAPHY......Page 313 INDEX......Page 325