LEADER 04468nam 2200541 450 001 9910720067503321 005 20240115151142.0 010 $a9783031094965$b(electronic bk.) 010 $z9783031094958 024 7 $a10.1007/978-3-031-09496-5 035 $a(MiAaPQ)EBC7243101 035 $a(Au-PeEL)EBL7243101 035 $a(DE-He213)978-3-031-09496-5 035 $a(OCoLC)1378936684 035 $a(PPN)26965559X 035 $a(EXLCZ)9926540746900041 100 $a20230801d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDomination in Graphs $eCore Concepts /$fTeresa W. Haynes, Stephen T. Hedetniemi, and Michael A. Henning 205 $aFirst edition. 210 1$aCham, Switzerland :$cSpringer,$d[2023] 210 4$d©2023 215 $a1 online resource (655 pages) 225 1 $aSpringer Monographs in Mathematics Series 311 08$aPrint version: Haynes, Teresa W. Domination in Graphs: Core Concepts Cham : Springer International Publishing AG,c2023 9783031094958 320 $aIncludes bibliographical references and index. 327 $a1. Introduction -- 2. Historic background -- 3. Domination Fundamentals -- 4. Bounds in terms of order and size, and probability -- 5. Bounds in terms of degree -- 6. Bounds with girth and diameter conditions -- 7. Bounds in terms of forbidden subgraphs -- 8. Domination in graph families : Trees -- 9. Domination in graph families: Claw-free graphs -- 10. Domination in regular graphs including Cubic graphs -- 11. Domination in graph families: Planar graph -- 12. Domination in graph families: Chordal, bipartite, interval, etc -- 13. Domination in grid graphs and graph products -- 14. Progress on Vizing's Conjecture -- 15. Sums and Products (Nordhaus-Gaddum) -- 16. Domination Games -- 17. Criticality -- 18. Complexity and Algorithms -- 19. The Upper Domination Number -- 20. Domatic Numbers (for lower and upper gamma) and other dominating partitions, including the newly introduced Upper Domatic Number -- 21. Concluding Remarks, Conjectures, and Open Problems. 330 $aThis monograph is designed to be an in-depth introduction to domination in graphs. It focuses on three core concepts: domination, total domination, and independent domination. It contains major results on these foundational domination numbers, including a wide variety of in-depth proofs of selected results providing the reader with a toolbox of proof techniques used in domination theory. Additionally, the book is intended as an invaluable reference resource for a variety of readerships, namely, established researchers in the field of domination who want an updated, comprehensive coverage of domination theory; next, researchers in graph theory who wish to become acquainted with newer topics in domination, along with major developments in the field and some of the proof techniques used; and, graduate students with interests in graph theory, who might find the theory and many real-world applications of domination of interest for masters and doctoral thesis topics. The focused coverage also provides a good basis for seminars in domination theory or domination algorithms and complexity. The authors set out to provide the community with an updated and comprehensive treatment on the major topics in domination in graphs. And by Jove, they?ve done it! In recent years, the authors have curated and published two contributed volumes: Topics in Domination in Graphs, © 2020 and Structures of Domination in Graphs, © 2021. This book rounds out the coverage entirely. The reader is assumed to be acquainted with the basic concepts of graph theory and has had some exposure to graph theory at an introductory level. As graph theory terminology sometimes varies, a glossary of terms and notation is provided at the end of the book. 410 0$aSpringer monographs in mathematics. 606 $aDomination (Graph theory) 606 $aTeoria de grafs$2thub 608 $aLlibres electrònics$2thub 615 0$aDomination (Graph theory) 615 7$aTeoria de grafs 676 $a511.5 700 $aHaynes$b Teresa W.$f1953-$061766 702 $aHedetniemi$b S. T. 702 $aHenning$b Michael A. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910720067503321 996 $aDomination in Graphs$93419642 997 $aUNINA