{"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}
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
图论基础概论，Jonathan L. Gross和Jay Yellen图与有向图族，Lowell W. Beineke图论历史，Robin J. Wilson图表示图的计算机表示，Alfred V. Aho图同构，Brendan D. McKay重构问题，Josef Lauri递归构造图，Richard B. Borie, R. Gary Parker和Craig A. Tovey结构图论，Maria Chudnovsky有向图基本有向图模型和性质，Jay Yellen有向无环图，Stephen B. Maurer比赛，K.B. Reid连通性和可穿越性连通性和结构，Camino Balbuena, Josep Fabrega和Miguel Angel Fiol eulergraph, Herbert Fleischner中国邮差问题，R. Gary Parker和Richard B. Borie DeBruijn图和序列，A.K. Dewdney hamilton图，Ronald J. Gould旅行商问题，Gregory Gutin:连性的进一步主题，Josep Fabrega和Miguel Angel Fiol着色和相关主题图着色，Zsolt Tuza图着色的进一步主题，Zsolt Tuza独立和团，Gregory Gutin因子和分解，Michael Plummer在时间表中的应用，Edmund Burke, Dominique de Werra和Jeffrey Kingston的修饰标记，Joseph A. Gallian代数图论自同构，Mark E. Watkins Cayley图，Brian Alspach列举，Paul K. Stockmeyer图与向量空间，Krishnaiyan“KT”Thulasiraman谱图理论，Michael Doob图论中的矩阵方法，James Oxley拓扑图论曲面图，Tomaz Pisanski和Primoz Potocnik最小格和最大格，Jianer Chen格分布，Jonathan L. Gross电压图，Jonathan L. Gross群的格，Thomas W. Tucker图，Roman Nedela和Martin Skoviera代表性，Dan Archdeacon三角剖分，Seiya Negami图与有限几何、Arthur T. White交叉数、R. Bruce Richter和Gelasio Salazar解析图论、极值图论、Bela Bollobas和Vladimir Nikiforov随机图、Nicholas Wormald Ramsey图论、Ralph J. Faudree的概率方法、Alan Frieze和Po-Shen Loh图极限、Bojan Mohar图中的测量距离、Gary Chartrand和Ping控制图、Teresa W. Haynes和Michael A. Henning公差图、Martin Charles Golumbic Bandwidth, Robert C. Brigham追逃问题，Richard B. Borie, Sven Koenig和Craig A. Tovey图在计算机科学搜索中的应用，Harold N. Gabow动态图算法，Camil Demetrescu, Irene Finocchi和Giuseppe F. Italiano图的绘图，Emilio Di Giacomo, Giuseppe Liotta和Roberto Tamassia递归构造图的算法，Richard B. Borie, R. Gary Parker和Craig A. Tovey模糊图，John N. Mordeson和D.S. Malik扩展图，Mike Krebs和Anthony Shaheen可见性图，Alice M. Dean和Joan P. Hutchinson网络和流量最大流量，Clifford Stein最小成本流，Lisa Fleischer匹配和分配，Jay Sethuraman和Douglas R. Shier通信网络复杂网络，Anthony Bonato和Fan Chung广播和绯闻，Hovhannes A. Harutyunyan, Arthur L. Liestman, Joseph G. Peters和Dana Richards通信网络设计模型，Prakash Mirchandani和David Simchi-Levi的图论网络科学，David C. Arney和Steven B. Horton自然科学与过程化学图论，Ernesto Estrada和Danail Bonchev图论与生物学之间的联系，Jacek Blazewicz, Marta Kasprzak和Nikos Vlassis索引术语表出现在每章的末尾。
{"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}
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
{"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}
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.
{"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}
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