Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity.

This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.

1. Introduction.- 2. Results for some graph classes.- 3. Algorithm and complexity.- 4. Sharp bounds of the generalized (edge-) connectivity.- 5. Graphs with given generalized connectivity.- 6. Nordhaus-Gaddum-type results.- 7. Results for graph products.- 8. Maximum generalized local connectivity.- 9. Generalized connectivity for random graphs.- Bibliography.- Index.