Topics in Domination in Graphs de Teresa W. Haynes

Topics in Domination in Graphs: Developments in Mathematics, cartea 64

Editat de Teresa W. Haynes, Stephen T. Hedetniemi, Michael A. Henning

en Limba Engleză Paperback – 10 noi 2021

Relevanța acestui volum pentru cercetătorii și studenții la nivel de doctorat în matematică discretă este definită prin rigoarea cu care tratează ramificațiile complexe ale teoriei grafurilor, fiind un instrument de referință pentru cei care urmăresc acreditări academice în combinatorică. Observăm o organizare metodică a celor 16 contribuții, care ghidează cititorul de la un glosar esențial de termeni, în capitolul introductiv semnat de Teresa W. Haynes, către modele teoretice avansate și tehnici de demonstrație specifice. Subliniem faptul că lucrarea nu se limitează la o expunere teoretică, ci integrează probleme deschise ce pot constitui baza unor noi direcții de cercetare.

Structura progresivă a volumului Topics in Domination in Graphs permite explorarea unor parametri nișați, precum dominația „Romană”, dominația de putere sau funcțiile de dominație semnate și minus, capitolele fiind semnate de experți de talie mondială. Această abordare completează perspectiva oferită de Domination in Graphs: Core Concepts, adăugând o analiză detaliată a variantelor moderne de dominație (precum cea „restrained” sau „rainbow”) pe care manualul de concepte fundamentale le tratează doar tangențial.

În contextul operei editorilor, acest volum se plasează ca o continuare firească a lucrării Structures of Domination in Graphs, menținând standardele de terminologie, dar extinzând aria de aplicabilitate către jocuri de dominație și parametri fracționari. Descoperim aici o sinteză actualizată a rezultatelor recente, oferind cititorului nu doar teoreme, ci și „trusa de scule” logică necesară pentru a aborda conjecturile nerezolvate din domeniu.

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Specificații

ISBN-13: 9783030511197
ISBN-10: 3030511197
Pagini: 545
Ilustrații: VIII, 545 p. 50 illus., 49 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.77 kg
Ediția:1st ed. 2020
Editura: Springer International Publishing
Colecția Springer
Seria Developments in Mathematics

Locul publicării:Cham, Switzerland

De ce să citești această carte

Recomandăm această lucrare matematicienilor specializați în combinatorică și studenților la masterat sau doctorat care au nevoie de o bază solidă pentru cercetare. Cititorul câștigă acces la o colecție sistematizată de tehnici de demonstrație și probleme deschise actualizate până în 2020. Este o resursă esențială pentru a înțelege cum evoluează conceptele de dominație de la formele clasice la aplicații moderne complexe în rețele și sisteme de putere.

Despre autor

Teresa W. Haynes, Stephen T. Hedetniemi și Michael A. Henning sunt figuri centrale în teoria grafurilor, cu o activitate editorială și de cercetare vastă sub egida Springer. Teresa W. Haynes este recunoscută pentru eforturile de standardizare a terminologiei în domeniul dominației, fiind autoarea unor monografii de referință. Stephen T. Hedetniemi, în onoarea căruia au fost publicate volume omagiale precum cele semnate de Gary Chartrand, a influențat decisiv direcțiile de studiu în colorarea și dominația grafurilor. Michael A. Henning completează echipa cu o expertiză profundă în parametrii de dominație totală și distanță, contribuind la consolidarea seriei Developments in Mathematics.

Descriere scurtă

This volume comprises 16 contributions that present advanced topics in graph domination, featuring open problems, modern techniques, and recent results. The focus is on primary dominating sets such as paired domination, connected domination, restrained domination, dominating functions, Roman domination, and power domination. Additionally, surveys include known results with a sample of proof techniques for each parameter. Of extra benefit to the reader, the first chapter includes a glossary of commonly used terms; the second chapter provides an overview of models of domination from which the parameters are defined.
The book is intended to provide a reference for established researchers in the fields of domination and graph theory and graduate students who wish to gain knowledge of the topics covered as well as an overview of the major accomplishments in the field and proof techniques used.

Cuprins

Glossary of Common Terms(W. Haynes).- Models of Domination in Graphs(W. Haynes).- Paired Domination in Graphs(W. Haynes).- Connected domination (Chellali).- Restrained and total restrained domination in graphs(H. Hattingh).- Multiple domination(Hansberg).- Distance Domination in Graphs(A. Henning).- Locating-Domination and Identification(Lobstein).- Signed and Minus Dominating Functions in Graphs(Shan).- Fractional Dominating Parameters(A Henning).- Roman domination in graphs(Chellali).- Rainbow Domination in Graphs(Bresar).- Eternal and Secure Domination in Graphs(M Mynhardt).- Strati ed Domination(Chartrand).- Global Domination(C. Brigham).- Power domination in graphs(Dorbec).

Notă biografică

Teresa W. Haynes has focused her research on domination in graphs for over 30 years and is perhaps best known for coauthoring the 1998 book Fundamentals of Domination in Graphs and the companion volume Domination in Graphs: Advanced Topics. She has also co-edited 2 volumes in Springer’s Problem Books in Mathematics Graph Theory: Favorite Conjectures and Open Problems. Haynes is also a co-author of the Springer Briefs in Mathematics From Domination to Coloring: The Graph Theory of Stephen T. Hedetniemi. Upon receiving her PhD from the University of Central Florida in 1988, she joined East Tennessee State University, where she is currently professor in the Department of Mathematics and Statistics. Haynes has coauthored more than 200 papers on domination and domination-related concepts, which introduced some of the most studied concepts in domination, such as power domination, paired domination, double domination, alliances and broadcasts in graphs, and stratified domination.

Stephen T. Hedetniemi is one of the earliest pioneers of domination in graphs along with E. J. Cockayne, who together proposed the theory of domination in graphs, in one of the most cited papers in the field in 1977. He received his PhD from the University of Michigan in 1966, with two world-class advisors, graph theorist Frank Harary, and the pioneer of genetic algorithms and MacArthur Fellowship winner, John Holland. He coauthored, the first book on domination in 1988 Fundamentals of Domination in Graphs, and co-edited a second book, Domination in Graphs: Advanced Topics. He also co-edited 2 volumes in Springer’s Problem Books in Mathematics Graph Theory: Favorite Conjectures and Open Problems. Since 1974 he has coauthored more than 300 papers, 180 of which are on domination and domination-related concepts. Hedetniemi has introduced some of the most-studied concepts in domination theory, including total domination, independent domination, irredundance, Roman domination, power domination, alliances in graphs, signed and minus domination, fractional domination, domatic numbers, domination in grid graphs and chessboards, the first domination algorithms, the first domination NP-completeness results, and the first self-stabilizing domination algorithms. After leaving the University of Michigan, he taught computer science at the University of Iowa, and the University of Virginia, spent a visiting year at the University of Victoria with E. J. Cockayne, and then became department head of Computer and information Science at the University of Oregon. Since 1982 has been at Clemson University, where he served a five-year term as department head, and served on the Executive Committee of the Computing Accreditation Commission of ABET, Inc. He is currently Emeritus Professor of Computer Science in the School of Computing at Clemson University.

Michael A. Henning has devoted much of his research interests to the field of domination theory in graphs. He has been both plenary and invited speakers at several international conferences and is a prolific researcher having published over 460 papers to date in international mathematics journals. Henning was born and schooled in South Africa having obtained his PhD at the University of Natal in April 1989. In January 1989, he started his academic career as a lecturer at the University of Zululand, before accepting a lectureship in mathematics at the former University of Natal in January 1991. In January 2000, he was appointed a full professor at the University of Natal, which later merged with the University of Durban-Westville to form the University of KwaZulu-Natal in January 2004. After spending almost 20 years at the University of KwaZulu-Natal and one of its predecessors, the University of Natal, Michael moved to the University of Johannesburg in May 2010 as a research professor. He co-authored a Springer Briefs in Mathematics From Domination to Coloring: The Graph Theory of Stephen T. Hedetniemi and co-authored the Springer Monographs in Mathematics book Total Domination in Graphs and in 2020, he co-authored Springer’s Developments in Mathematics book Transversals in Linear Uniform Hypergraphs.