UID:
almafu_9960119733802883
Umfang:
1 online resource (x, 176 pages) :
,
digital, PDF file(s).
ISBN:
0-511-66639-X
Serie:
Cambridge tracts in theoretical computer science ; 49
Inhalt:
First published in 1999, this book combines traditional graph theory with the matroidal view of graphs and throws light on mathematical aspects of network analysis. This approach is called here hybrid graph theory. This is essentially a vertex-independent view of graphs naturally leading into the domain of graphoids, a generalisation of graphs. This enables the authors to combine the advantages of both the intuitive view from graph theory and the formal mathematical tools from the theory of matroids. A large proportion of the material is either new or is interpreted from a fresh viewpoint. Hybrid graph theory has particular relevance to electrical network analysis, which was one of the earliest areas of application of graph theory. It was essentially out of developments in this area that hybrid graph theory evolved.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
1. Two Dual Structures of a Graph. 1.1. Basic concepts of graphs. 1.2. Cuts and circs. 1.3. Cut and circ spaces. 1.4. Relationships between cut and circ spaces. 1.5. Edge-separators and connectivity.
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1.6. Equivalence relations among graphs. 1.7. Directed graphs. 1.8. Networks and multiports. 1.9. Kirchhoff's laws. 1.10. Bibliographic notes -- 2. Independence Structures. 2.1. The graphoidal point of view.
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2.2. Independent collections of circs and cuts. 2.3. Maximal circless and cutless sets. 2.4. Circ and cut vector spaces. 2.5. Binary graphoids and their representations. 2.6. Orientable binary graphoids and Kirchhoff's laws.
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2.7. Mesh and nodal analysis. 2.8. Bibliographic notes -- 3. Basoids. 3.1. Preliminaries. 3.2. Basoids of graphs. 3.3. Transitions from one basoid to another. 3.4. Minor with respect to a basoid. 3.5. Principal sequence.
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3.6. Principal minor and principal partition. 3.7. Hybrid rank and basic pairs of subsets. 3.8. Hybrid analysis of networks. 3.9. Procedure for finding an optimal basic pair. 3.10. Bibliographic notes -- 4. Pairs of Trees.
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4.1. Diameter of a tree. 4.2. Perfect pairs of trees. 4.3. Basoids and perfect pairs of trees. 4.4. Superperfect pairs of trees. 4.5. Unique solvability of affine networks. 4.6. Bibliographic notes.
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5. Maximally Distant Pairs of Trees. 5.1. Preliminaries. 5.2. Minor with respect to a pair of trees. 5.3. Principal sequence. 5.4. The principal minor. 5.5. Hybrid pre-rank and the principal minor.
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5.6. Principal partition and Shannon's game. 5.7. Bibliographic notes.
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English
Weitere Ausg.:
ISBN 0-521-10659-1
Weitere Ausg.:
ISBN 0-521-46117-0
Sprache:
Englisch
URL:
https://doi.org/10.1017/CBO9780511666391
