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GraphTheoretic Approach to the Solvability
Chapter 3 GraphTheoretic Approach to the Controllability
5 other sections not shown
algebraically independent algorithm arc-set arcs associated bipartite graph assume assumption auxiliary graph auxiliary network block-triangular blocks coefficient matrix column-set columns combinatorial canonical form computation consider corresponding decomposition defined denoted descriptor system 12.3 dimensional analysis Dulmage-Mendelsohn decomposition dynamical system electrical network equivalent Example exists expressed extended form 12.2 feedback vertex set flow f given graph G graph-theoretic Hasse diagram independent over Q independent-flow problem Jacobian matrix layered mixed matrix M-components mathematical matrix D(s matroid-theoretic max-flow min-cut theorem maximum flow maximum independent flow maximum matching Menger-type complete linking minimum minimum cuts Murota nonsingular nonvanishing entries obtained partial order permutation permutation matrices polymatroid Proof Prop Proposition rational numbers representation graph resp respect row-set signal-flow graph standard form 12.1 structural analysis structural controllability structural solvability subgraph submatrix subproblems subset system of equations term-rank Theorem transformation type DD vertex vertex-induced subgraph vertex-set vertices