Graph Theory: Flows, MatricesGraph Theory: Flows, Matrices covers a number of topics in graph theory that are important in the major areas of application. It provides graph theoretic tools that can be readily and efficiently applied to problems in operational research, computer science, electrical engineering, and economics. Emphasizing didactic principles, the book derives theorems and proofs from a detailed analysis of the structure of graphs. The easy-to-follow algorithms can be readily converted to computer codes in high-level programming languages. Requiring knowledge of the basic concepts of graph theory and a familiarity with some simple results, the book also includes 100 exercises with solutions to help readers gain experience and 131 diagrams to aid in the understanding of concepts and proofs. |
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A₁ according to Theorem adjacency matrix Algorithm augmenting path B₁ B₂ bipartite graph block bypass path circuit matrix circuit of G columns complete bipartite graph complete graph completes the proof connected graph defined denote directed graph dual dual graph e₁ edge p,q edge xy-cut edge-capacity function edge-disjoint xy-paths edges incident edges of G eigenvalue eigenvector electrical network elements endpoints feasible following theorem function f G containing G₁ G₂ graph containing graph G Hence implies included inner vertex integer function K₁ linear linearly independent maximal number maximal value minimal cost Möbius ladder n-connected non-negative number of edges obtained P₁ partition pq-path problem proof of Theorem proved R₁ reduced incidence matrix row vectors set of edges set of vertices shown in figure simple graph subgraph of G subset Theorem 11 transportation V₁ verify vertex-disjoint vertices of G xy-flow xy-paths xy-paths in G yields zero
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References to this book
Nichtlineare Regelungssysteme: ein differentialalgebraischer Ansatz ; mit 13 ... Torsten Wey No preview available - 2002 |