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Hybrid graph theory and network analysis

Author: Ladislav Novak; Alan Gibbons
Publisher: Cambridge ; New York : Cambridge University Press, ©1999.
Series: Cambridge tracts in theoretical computer science.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This book combines traditional graph theory with the matroid view of graphs in order to throw light on the mathematical approach to network analysis. The authors include many new results as well as  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Ladislav Novak; Alan Gibbons
ISBN: 0521461170 9780521461177
OCLC Number: 39523063
Description: x, 176 pages : illustrations ; 24 cm.
Contents: 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. 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. 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. 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. 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. 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. 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. 5.6. Principal partition and Shannon's game. 5.7. Bibliographic notes.
Series Title: Cambridge tracts in theoretical computer science.
Responsibility: Ladislav Novak, Alan Gibbons.
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"The book is well organized and presented, and is a welcome addition to the field." Mathematical Reviews

 
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