LEADER 05713nam 22006855 450 001 9910574082803321 005 20251113195600.0 010 $a3-031-03857-6 024 7 $a10.1007/978-3-031-03857-0 035 $a(MiAaPQ)EBC7008860 035 $a(Au-PeEL)EBL7008860 035 $a(CKB)23231029300041 035 $aEBL7008860 035 $a(AU-PeEL)EBL7008860 035 $a(PPN)269149414 035 $a(OCoLC)1325717919 035 $a(DE-He213)978-3-031-03857-0 035 $a(EXLCZ)9923231029300041 100 $a20220603d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGraph and Network Theory $eAn Applied Approach using Mathematica® /$fby Michael A. Henning, Jan H. van Vuuren 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (782 pages) 225 1 $aSpringer Optimization and Its Applications,$x1931-6836 ;$v193 300 $aDescription based upon print version of record. 311 08$aPrint version: Henning, Michael A. Graph and Network Theory Cham : Springer International Publishing AG,c2022 9783031038563 320 $aIncludes bibliographical references and index. 327 $aPreface -- List of Algorithms -- List of Bibliographical Notes -- Part 1. Topics in network optimisation -- 1. An introduction to graphs -- 2. Graph connectedness -- 3. Algorithmic complexity -- 4. Optimal paths -- 5. Trees -- 6. Location problems -- 7. Maximum flow networks -- 8. Minimum-cost network flows -- Part 2. Topics in classical graph theory -- 9. Matchings -- 10. Eulerian graphs -- 11. Hamiltonian graphs -- 12. Graph connectivity -- 13. Planarity -- 14. Graph colouring -- 15. Oriented graphs. Part 3. Topics in modern graph theory -- 16. Domination in graphs -- 17. Ramsey Theory -- 18. Extremal graph theory -- 19. Graph enumeration -- 20. The probabilistic method -- Index. 330 $aThis textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader.Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method. 410 0$aSpringer Optimization and Its Applications,$x1931-6836 ;$v193 606 $aOperations research 606 $aManagement science 606 $aGraph theory 606 $aDiscrete mathematics 606 $aOperations Research, Management Science 606 $aGraph Theory 606 $aApplications of Discrete Mathematics 615 0$aOperations research. 615 0$aManagement science. 615 0$aGraph theory. 615 0$aDiscrete mathematics. 615 14$aOperations Research, Management Science. 615 24$aGraph Theory. 615 24$aApplications of Discrete Mathematics. 676 $a511.5 676 $a511.5 700 $aHenning$b Mike$01270981 702 $aVan Vuuren$b J. H. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910574082803321 996 $aGraph and network theory$92994199 997 $aUNINA