Hybrid graph theory and network analysis [EBook] / Ladislav Novak, Alan Gibbons.
Hybrid graph theory and network analysis [EBook] / Ladislav Novak, Alan Gibbons.
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 vertexindependent view of graphs naturally leading into the do...
Personal Name(s):  Novak, Ladislav, (author) 

Gibbons, Alan, (author)  
Imprint: 
Cambridge :
Cambridge University Press,
1999

Physical Description: 
1 online resource (x, 176 pages) 
Note: 
englisch 
ISBN: 
9780511666391 9780521461177 9780521106597 
Series Title: 
Cambridge tracts in theoretical computer science ;
49 
Subject (LOC):  
Full Text 
Table of 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. Edgeseparators 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 prerank and the principal minor.
 5.6. Principal partition and Shannon's game. 5.7. Bibliographic notes.