Издательство Marcel Dekker, 1998, -455 pp.
The result of these objectives is a book that is appropriate for use at several different levels. Containing the only existing comprehensive bibliography on domination, it is a valuable reference book. It is suitable as a textbook for graduate level courses in graph theory and could also be used by advanced un- undergraduates. As a textbook, it is complete with exercises ranging in level from introductory and easy to advanced and difficult. The book is self-contained, with the necessary basic definitions and preliminary graph theoretic results presented in the prolegomenon. A second course in graph theory can treat the prolegomenon as a reference and begin with Chapter
1. A majority of the readers of this text will have had some exposure —if not a full course— to graph theory but it could well be used for a first course in graph theory. Instructors who want to use it in a first course can expand beyond subset problems by developing the topics in the prolegomenon. It can also be used as a supple- supplemental text for courses in graph theory, combinatorics, and related areas. As a definitive reference guide on domination in graphs, it will be a valuable tool to researchers and advanced graduate students. They can use the book to familiarize themselves with the subject, the research techniques, and major research accomplishments in the field. Advanced graduate students will find many topics that can be developed into masters theses and Ph.D. dissertations.
Prolegomenon.
Introduction.
Bounds on the Domination Number.
Domination, Independence, and Irredundance.
Efficiency, Redundancy, and Their Duals.
Changing and Unchanging Domination.
Conditions on the Dominating Set.
arieties of Domination.
Multiproperty and Multiset Parameters.
Sums and Products of Parameters.
Dominating Functions.
Frameworks for Domination.
Domination Complexity and Algorithms.
The result of these objectives is a book that is appropriate for use at several different levels. Containing the only existing comprehensive bibliography on domination, it is a valuable reference book. It is suitable as a textbook for graduate level courses in graph theory and could also be used by advanced un- undergraduates. As a textbook, it is complete with exercises ranging in level from introductory and easy to advanced and difficult. The book is self-contained, with the necessary basic definitions and preliminary graph theoretic results presented in the prolegomenon. A second course in graph theory can treat the prolegomenon as a reference and begin with Chapter
1. A majority of the readers of this text will have had some exposure —if not a full course— to graph theory but it could well be used for a first course in graph theory. Instructors who want to use it in a first course can expand beyond subset problems by developing the topics in the prolegomenon. It can also be used as a supple- supplemental text for courses in graph theory, combinatorics, and related areas. As a definitive reference guide on domination in graphs, it will be a valuable tool to researchers and advanced graduate students. They can use the book to familiarize themselves with the subject, the research techniques, and major research accomplishments in the field. Advanced graduate students will find many topics that can be developed into masters theses and Ph.D. dissertations.
Prolegomenon.
Introduction.
Bounds on the Domination Number.
Domination, Independence, and Irredundance.
Efficiency, Redundancy, and Their Duals.
Changing and Unchanging Domination.
Conditions on the Dominating Set.
arieties of Domination.
Multiproperty and Multiset Parameters.
Sums and Products of Parameters.
Dominating Functions.
Frameworks for Domination.
Domination Complexity and Algorithms.