Graph Theory: Flows, Matrices
Graph 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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according to Theorem adjacency matrix Algorithm bipartite graph block bypass path circuit matrix circuit of G columns complete bipartite graph complete graph completes the proof connected graph containing c vertices cutset matrix defined delete the edges denote directed graph dual dual graph edge xy-cut edge-capacity function edge-disjoint xy-paths edges incident edges of G eigenvalue eigenvector electrical network elements endpoints equivalence relation feasible following theorem G containing graph containing graph G Hence implies included inner vertex integer function linear linearly independent loop matroid maximal number maximal value minimal cost n-connected non-negative non-singular non-zero number of edges obtained partition pg-path problem proof of Theorem proved reduced incidence matrix respectively row vectors set of edges set of vertices shown in figure simple graph spectrum square matrix subgraph of G subset Theorem 11 Theorem 25 transportation verify vertex xy-cut vertex-disjoint vertices of G xy-paths in G yields zero
Page 276 - Kuh, ES, and Rohrer, RA, The state variable approach to network analysis, Proc.