Discrete Mathematics and Its Applications最新文献

{"title":"Combinatorics of Permutations, Second Edition","authors":"M. Bóna","doi":"10.1201/B12210","DOIUrl":"https://doi.org/10.1201/B12210","url":null,"abstract":"","PeriodicalId":430406,"journal":{"name":"Discrete Mathematics and Its Applications","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125665500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Handbook of graph theory","authors":"J. Gross","doi":"10.1201/9780203490204","DOIUrl":"https://doi.org/10.1201/9780203490204","url":null,"abstract":"Introduction to Graphs Fundamentals of Graph Theory, Jonathan L. Gross and Jay Yellen Families of Graphs and Digraphs, Lowell W. Beineke History of Graph Theory, Robin J. Wilson Graph Representation Computer Representation of Graphs, Alfred V. Aho Graph Isomorphism, Brendan D. McKay The Reconstruction Problem, Josef Lauri Recursively Constructed Graphs, Richard B. Borie, R. Gary Parker, and Craig A. Tovey Structural Graph Theory, Maria Chudnovsky Directed Graphs Basic Digraph Models and Properties, Jay Yellen Directed Acyclic Graphs, Stephen B. Maurer Tournaments, K.B. Reid Connectivity and Traversability Connectivity Properties and Structure, Camino Balbuena, Josep Fabrega, and Miguel Angel Fiol Eulerian Graphs, Herbert Fleischner Chinese Postman Problems, R. Gary Parker and Richard B. Borie DeBruijn Graphs and Sequences, A.K. Dewdney Hamiltonian Graphs, Ronald J. Gould Traveling Salesman Problems, Gregory Gutin Further Topics in Connectivity, Josep Fabrega and Miguel Angel Fiol Colorings and Related Topics Graph Coloring, Zsolt Tuza Further Topics in Graph Coloring, Zsolt Tuza Independence and Cliques, Gregory Gutin Factors and Factorization, Michael Plummer Applications to Timetabling, Edmund Burke, Dominique de Werra, and Jeffrey Kingston Graceful Labelings, Joseph A. Gallian Algebraic Graph Theory Automorphisms, Mark E. Watkins Cayley Graphs, Brian Alspach Enumeration, Paul K. Stockmeyer Graphs and Vector Spaces, Krishnaiyan \"KT\" Thulasiraman Spectral Graph Theory, Michael Doob Matroidal Methods in Graph Theory, James Oxley Topological Graph Theory Graphs on Surfaces, Tomaz Pisanski and Primoz Potocnik Minimum Genus and Maximum Genus, Jianer Chen Genus Distributions, Jonathan L. Gross Voltage Graphs, Jonathan L. Gross The Genus of a Group, Thomas W. Tucker Maps, Roman Nedela and Martin Skoviera Representativity, Dan Archdeacon Triangulations, Seiya Negami Graphs and Finite Geometries, Arthur T. White Crossing Numbers, R. Bruce Richter and Gelasio Salazar Analytic Graph Theory Extremal Graph Theory, Bela Bollobas and Vladimir Nikiforov Random Graphs, Nicholas Wormald Ramsey Graph Theory, Ralph J. Faudree The Probabilistic Method, Alan Frieze and Po-Shen Loh Graph Limits, Bojan Mohar Graphical Measurement Distance in Graphs, Gary Chartrand and Ping Zhang Domination in Graphs, Teresa W. Haynes and Michael A. Henning Tolerance Graphs, Martin Charles Golumbic Bandwidth, Robert C. Brigham Pursuit-Evasion Problems, Richard B. Borie, Sven Koenig, and Craig A. Tovey Graphs in Computer Science Searching, Harold N. Gabow Dynamic Graph Algorithms, Camil Demetrescu, Irene Finocchi, and Giuseppe F. Italiano Drawings of Graphs, Emilio Di Giacomo, Giuseppe Liotta, and Roberto Tamassia Algorithms on Recursively Constructed Graphs, Richard B. Borie, R. Gary Parker, and Craig A. Tovey Fuzzy Graphs, John N. Mordeson and D.S. Malik Expander Graphs, Mike Krebs and Anthony Shaheen Visibility Graphs, Alice M. Dean and Joan P. Hutchinson Networks and Flows Maximum F","PeriodicalId":430406,"journal":{"name":"Discrete Mathematics and Its Applications","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133121761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spanning trees and optimization problems","authors":"B. Wu, K. Chao","doi":"10.5860/choice.42-1619a","DOIUrl":"https://doi.org/10.5860/choice.42-1619a","url":null,"abstract":"SPANNING TREES Counting Spanning Trees MINIMUM SPANNING TREES Introduction Bor Degreesuvka's Algorithm Prim's Algorithm Kruskal's Algorithm Applications Summary Bibliographic Notes and Further Reading Exercises SHORTEST-PATHS TREES Introduction Dijkstra's Algorithm The Bellman-Ford Algorithm Applications Summary Bibliographic Notes and Further Reading Exercises MINIMUM ROUTING COST SPANNING TREES Introduction Approximating by a Shortest-Paths Tree Approximating by a General Star A Reduction to the Metric Case A Polynomial Time Approximation Scheme Applications Summary Bibliographic Notes and Further Reading Exercises OPTIMAL COMMUNICATION SPANNING TREES Introduction Product-Requirement Sum-Requirement Multiple Sources Applications Summary Bibliographic Notes and Further Reading Exercises BALANCING THE TREE COSTS Introduction Light Approximate Shortest-Paths Trees Light Approximate Routing Cost Spanning Trees Applications Summary Bibliographic Notes and Further Reading Exercises STEINER TREES AND SOME OTHER PROBLEMS Steiner Minimal Trees Trees and Diameters Maximum Leaf Spanning Trees Some Other Problems Bibliographic Notes and Further Reading Exercises REFERENCES INDEX","PeriodicalId":430406,"journal":{"name":"Discrete Mathematics and Its Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125654187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Introduction to Enumerative and Analytic Combinatorics, Second Edition","authors":"M. Bóna","doi":"10.1201/b19267","DOIUrl":"https://doi.org/10.1201/b19267","url":null,"abstract":"","PeriodicalId":430406,"journal":{"name":"Discrete Mathematics and Its Applications","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116090788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An introduction to cryptography, Second Edition","authors":"R. Mollin","doi":"10.1201/9781420011241","DOIUrl":"https://doi.org/10.1201/9781420011241","url":null,"abstract":"As the title states the book by Johannes Buchmann provides an introduction to cryptography. Buchmann’s text in only 324 pages (excluding the appendices) presents a stand alone introduction to some modern cryptographic methods. The book begins with the mathematical background that will be used as foundation for the cryptographic methods discussed in this book. Chapter one explains the important properties of integers and the extended Euclidean algorithm. Chapter two includes some important algebraic definitions (groups, residue class, ring, fields,...). Also, it contains algorithms for fast evaluation of power products and the Chinese remainder theorem. Probability theory and Shannon’s view of perfect secrecy are presented in chapter 4. There are three chapters discussing symmetric cryptography and to be more specific they are devoted to block ciphers. Chapter 3 explains the meaning of cryptosystems and gives some different encryption schemes. For the symmetric cryptography the author just defines the structure of stream ciphers and provides two examples, whereas he explains the block cipher in more details. Moreover chapter 5 and chapter 6 represent a complete study to the most famous block ciphers DES and AES, respectively. In the next four chapters, the author discusses asymmetric cryptography (public key cryptography). Since many public key cryptosystems use large prime numbers, the author gives more additional mathematical preliminaries for the prime number generation and some algorithms used for testing the primality of large numbers in chapter 7. The idea of public key cryptosystems and a description to the most important schemes are given in chapter 8, for examples RSA and ElGamal. The security of RSA is based on the difficulty of the factorization problem and is studied in chapter 9. It is focusing on the quadratic sieve algorithm and providing an estimation to the efficiency of it and some other factoring algorithms. Similarly, in chapter 10 the security analysis of ElGamal cryptosystem is discussed by analyzing the algorithms that solve the discrete logarithm problem.","PeriodicalId":430406,"journal":{"name":"Discrete Mathematics and Its Applications","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121461061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}