https://mklab.gr/ Sun, 13 Sep 2026 04:03:10 +0000 MyBB https://mklab.gr/showthread.php?tid=1640 Mon, 17 Aug 2026 18:15:50 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1640 Graph Theory
Authors: J. A. (Adrian) Bondy and U. S. R. Murty
Publication: 2008
Publisher: Springer London
Series:Graduate Texts in Mathematics, Vol. 244
Length: about 650 pages
ISBN: 978-1-84628-969-9 

Graph Theory by Bondy and Murty is a comprehensive and rigorous introduction to one of the central areas of discrete mathematics. Intended primarily for advanced undergraduate and beginning graduate students in mathematics and computer science, the book develops graph theory systematically while maintaining the intuitive and visual character that makes the subject attractive. It begins with fundamental ideas about graphs, subgraphs, connectedness and trees, then develops major themes including network flows, connectivity, planar graphs, the Four-Colour Problem, independent sets and cliques, vertex and edge colouring, matchings, Hamiltonian cycles, coverings and packings, electrical networks, and integer flows.

A particularly strong feature is the emphasis on mathematical reasoning rather than simply collecting theorems. Bondy and Murty repeatedly introduce proof techniques, demonstrate how they work in important results, and then reinforce them through a substantial collection of exercises of varying difficulty. The presentation also connects pure graph theory with applications in computer science, combinatorial optimization, operations research and communication networks. Algorithmic ideas and computational complexity therefore appear naturally alongside the theoretical mathematics. This makes the book valuable not only for learning what the important results of graph theory are, but also for learning how graph theorists approach and solve problems. 

The text goes beyond a conventional introductory textbook. Its later and more advanced sections introduce readers to research-level ideas, and the authors explicitly discuss challenging and unsolved problems. This gives the book an unusual progression: a student can use selected sections for a first serious course, while a more experienced reader can continue deeper into individual chapters as preparation for research. The Mathematical Association of America described the 2008 book as a substantial reworking and expansion of Bondy and Murty's earlier classic Graph Theory with Applications, noting its breadth in both theory and applications. 

Key takeaways

• Broad and rigorous: Covers most of the major areas of classical graph theory while reaching into advanced topics and open problems.
  
• Proof-oriented: Particularly valuable for developing techniques of mathematical proof and combinatorial problem solving.
  
• Theory meets algorithms: Builds connections among pure mathematics, algorithms, optimization, networks and computer science.
  
• Best suited to serious study: It is more demanding than a casual introduction, but an excellent choice for advanced undergraduates, graduate students, self-study, or someone preparing to pursue research in graph theory. 
  
  

Overall: ★★★★★ — A substantial modern graph-theory textbook that combines breadth, rigorous proofs, exercises and research-level perspectives particularly well.


Goodreads book page 

Springer book page]]> Graph Theory
Authors: J. A. (Adrian) Bondy and U. S. R. Murty
Publication: 2008
Publisher: Springer London
Series:Graduate Texts in Mathematics, Vol. 244
Length: about 650 pages
ISBN: 978-1-84628-969-9 

Graph Theory by Bondy and Murty is a comprehensive and rigorous introduction to one of the central areas of discrete mathematics. Intended primarily for advanced undergraduate and beginning graduate students in mathematics and computer science, the book develops graph theory systematically while maintaining the intuitive and visual character that makes the subject attractive. It begins with fundamental ideas about graphs, subgraphs, connectedness and trees, then develops major themes including network flows, connectivity, planar graphs, the Four-Colour Problem, independent sets and cliques, vertex and edge colouring, matchings, Hamiltonian cycles, coverings and packings, electrical networks, and integer flows.

A particularly strong feature is the emphasis on mathematical reasoning rather than simply collecting theorems. Bondy and Murty repeatedly introduce proof techniques, demonstrate how they work in important results, and then reinforce them through a substantial collection of exercises of varying difficulty. The presentation also connects pure graph theory with applications in computer science, combinatorial optimization, operations research and communication networks. Algorithmic ideas and computational complexity therefore appear naturally alongside the theoretical mathematics. This makes the book valuable not only for learning what the important results of graph theory are, but also for learning how graph theorists approach and solve problems. 

The text goes beyond a conventional introductory textbook. Its later and more advanced sections introduce readers to research-level ideas, and the authors explicitly discuss challenging and unsolved problems. This gives the book an unusual progression: a student can use selected sections for a first serious course, while a more experienced reader can continue deeper into individual chapters as preparation for research. The Mathematical Association of America described the 2008 book as a substantial reworking and expansion of Bondy and Murty's earlier classic Graph Theory with Applications, noting its breadth in both theory and applications. 

Key takeaways

• Broad and rigorous: Covers most of the major areas of classical graph theory while reaching into advanced topics and open problems.
  
• Proof-oriented: Particularly valuable for developing techniques of mathematical proof and combinatorial problem solving.
  
• Theory meets algorithms: Builds connections among pure mathematics, algorithms, optimization, networks and computer science.
  
• Best suited to serious study: It is more demanding than a casual introduction, but an excellent choice for advanced undergraduates, graduate students, self-study, or someone preparing to pursue research in graph theory. 
  
  

Overall: ★★★★★ — A substantial modern graph-theory textbook that combines breadth, rigorous proofs, exercises and research-level perspectives particularly well.


Goodreads book page 

Springer book page]]> https://mklab.gr/showthread.php?tid=1340 Sun, 26 Jul 2026 01:53:34 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1340
Galois’ Dream: Group Theory and Differential Equations
BY Michio Kuga

Summary

Galois’ Dream: Group Theory and Differential Equations, written by mathematician Michio Kuga and translated by Susan Addington and Motohico Mulase, offers an intuitive and engaging introduction to the deep connections bridging abstract algebra, topology, and complex analysis. Based on a series of undergraduate lectures originally delivered in Japan, the book aims to realize Évariste Galois' vision of applying symmetry and group theory beyond algebraic polynomial equations to the realm of differential equations.

 Rather than adhering to a rigid, formal textbook structure, Kuga employs informal prose, humorous illustrations, and visual analogies to demystify advanced topics such as monodromy groups, covering spaces, and Fuchsian differential equations. Readers are guided through foundational concepts including set theory, fundamental groups, Riemann surfaces, and analytic continuation, ultimately discovering how automorphic functions and discontinuous topological groups govern the global behavior of differential solutions. 

By demonstrating how distinct mathematical disciplines intersect and harmonize, the guide equips early-stage mathematics students with a broad conceptual overview, proving that abstract advanced mathematics can be both approachable and profoundly interconnected.

BOOK]]>
Galois’ Dream: Group Theory and Differential Equations
BY Michio Kuga

Summary

Galois’ Dream: Group Theory and Differential Equations, written by mathematician Michio Kuga and translated by Susan Addington and Motohico Mulase, offers an intuitive and engaging introduction to the deep connections bridging abstract algebra, topology, and complex analysis. Based on a series of undergraduate lectures originally delivered in Japan, the book aims to realize Évariste Galois' vision of applying symmetry and group theory beyond algebraic polynomial equations to the realm of differential equations.

 Rather than adhering to a rigid, formal textbook structure, Kuga employs informal prose, humorous illustrations, and visual analogies to demystify advanced topics such as monodromy groups, covering spaces, and Fuchsian differential equations. Readers are guided through foundational concepts including set theory, fundamental groups, Riemann surfaces, and analytic continuation, ultimately discovering how automorphic functions and discontinuous topological groups govern the global behavior of differential solutions. 

By demonstrating how distinct mathematical disciplines intersect and harmonize, the guide equips early-stage mathematics students with a broad conceptual overview, proving that abstract advanced mathematics can be both approachable and profoundly interconnected.

BOOK]]> https://mklab.gr/showthread.php?tid=1336 Sun, 26 Jul 2026 01:33:46 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1336 In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation 
BY William Cook

Summary

In In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation, mathematician William J. Cook provides an accessible exploration of the Traveling Salesman Problem (TSP)—the classic challenge of finding the shortest route to visit a set of cities exactly once and return to the starting point. Published by Princeton University Press, the book charts the historical trajectory of this deceptively simple puzzle from its nineteenth-century origins with Irish mathematician W. R. Hamilton to the cutting edge of theoretical computer science. 

Cook demystifies the computational complexity surrounding the TSP, explaining how it sits at the core of the famous P versus NP question and tests the limits of modern computing. Rather than relying on dense formulas, the author uses vivid historical anecdotes, intuitive explanations, and rich visual illustrations to examine algorithmic approaches such as linear programming and heuristic search methods. 

Beyond pure theory, the work highlights the practical significance of TSP techniques across diverse domains, including genome sequencing, computer processor design, logistics routing, and astronomical searches for exoplanets. By combining mathematical insights with engaging storytelling, Cook delivers a comprehensive overview of one of applied mathematics' most enduring and practical challenges.

BOOK]]> In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation 
BY William Cook

Summary

In In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation, mathematician William J. Cook provides an accessible exploration of the Traveling Salesman Problem (TSP)—the classic challenge of finding the shortest route to visit a set of cities exactly once and return to the starting point. Published by Princeton University Press, the book charts the historical trajectory of this deceptively simple puzzle from its nineteenth-century origins with Irish mathematician W. R. Hamilton to the cutting edge of theoretical computer science. 

Cook demystifies the computational complexity surrounding the TSP, explaining how it sits at the core of the famous P versus NP question and tests the limits of modern computing. Rather than relying on dense formulas, the author uses vivid historical anecdotes, intuitive explanations, and rich visual illustrations to examine algorithmic approaches such as linear programming and heuristic search methods. 

Beyond pure theory, the work highlights the practical significance of TSP techniques across diverse domains, including genome sequencing, computer processor design, logistics routing, and astronomical searches for exoplanets. By combining mathematical insights with engaging storytelling, Cook delivers a comprehensive overview of one of applied mathematics' most enduring and practical challenges.

BOOK]]> https://mklab.gr/showthread.php?tid=1335 Sun, 26 Jul 2026 01:29:02 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1335
Graphs and their Uses 
by Oystein Ore

Summary

Graphs and Their Uses, written by Øystein Ore and updated by Robin J. Wilson, serves as an introductory guide to graph theory designed for students, educators, and mathematics enthusiasts. The book breaks down fundamental concepts of discrete mathematics, exploring essential structures such as vertices, edges, trees, cycles, planar graphs, and directed networks. 

Rather than relying strictly on dense abstract proofs, it emphasizes intuitive visual problem-solving and practical real-world applications. Readers are guided through iconic mathematical puzzles and optimization challenges, including the Bridges of Königsberg problem, the Traveling Salesman Problem, job-applicant matchings, tournament structures, map coloring, and traffic routing systems. The updated edition modernizes notation while incorporating additional material on topics like interval graphs, shortest-route algorithms, and structural bracing frameworks. 

Through clear diagrams and structured explanations, the text demonstrates how graph theory models complex relations in logistics, social networks, game theory, and computer science. Ultimately, the guide offers a clear and accessible bridge between foundational mathematics and real-world network analysis.

BOOK]]>
Graphs and their Uses 
by Oystein Ore

Summary

Graphs and Their Uses, written by Øystein Ore and updated by Robin J. Wilson, serves as an introductory guide to graph theory designed for students, educators, and mathematics enthusiasts. The book breaks down fundamental concepts of discrete mathematics, exploring essential structures such as vertices, edges, trees, cycles, planar graphs, and directed networks. 

Rather than relying strictly on dense abstract proofs, it emphasizes intuitive visual problem-solving and practical real-world applications. Readers are guided through iconic mathematical puzzles and optimization challenges, including the Bridges of Königsberg problem, the Traveling Salesman Problem, job-applicant matchings, tournament structures, map coloring, and traffic routing systems. The updated edition modernizes notation while incorporating additional material on topics like interval graphs, shortest-route algorithms, and structural bracing frameworks. 

Through clear diagrams and structured explanations, the text demonstrates how graph theory models complex relations in logistics, social networks, game theory, and computer science. Ultimately, the guide offers a clear and accessible bridge between foundational mathematics and real-world network analysis.

BOOK]]> https://mklab.gr/showthread.php?tid=1330 Sun, 26 Jul 2026 01:07:56 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1330 Modern Graph Theory 
BY  Béla Bollobás

Summary

Modern Graph Theory by Béla Bollobás is an in-depth, rigorous textbook designed for serious students and researchers in mathematics and computer science. The book provides a modern and comprehensive account of the subject while emphasizing its profound connections to other areas of pure mathematics. Structured to engage readers and kindle academic interest, it balances technical precision with detailed descriptive passages that explain the underlying intuition behind major theorems. 

Alongside classical graph theory fundamentals, Bollobás covers advanced contemporary topics, including Szemerédi's Regularity Lemma and its applications, Shelah's extension of the Hales-Jewett Theorem, and the precise phase transitions occurring in random graph processes. It also highlights fascinating interdisciplinary bridges, such as the relationships between electrical networks and random walks on graphs, as well as the Tutte polynomial and knot theory. 

Complete with over 600 thoughtfully constructed exercises—ranging from introductory problems to deep challenges designed to stretch top mathematicians—the guide stands as an authoritative and complete foundation in modern graph theory.

BOOK]]> Modern Graph Theory 
BY  Béla Bollobás

Summary

Modern Graph Theory by Béla Bollobás is an in-depth, rigorous textbook designed for serious students and researchers in mathematics and computer science. The book provides a modern and comprehensive account of the subject while emphasizing its profound connections to other areas of pure mathematics. Structured to engage readers and kindle academic interest, it balances technical precision with detailed descriptive passages that explain the underlying intuition behind major theorems. 

Alongside classical graph theory fundamentals, Bollobás covers advanced contemporary topics, including Szemerédi's Regularity Lemma and its applications, Shelah's extension of the Hales-Jewett Theorem, and the precise phase transitions occurring in random graph processes. It also highlights fascinating interdisciplinary bridges, such as the relationships between electrical networks and random walks on graphs, as well as the Tutte polynomial and knot theory. 

Complete with over 600 thoughtfully constructed exercises—ranging from introductory problems to deep challenges designed to stretch top mathematicians—the guide stands as an authoritative and complete foundation in modern graph theory.

BOOK]]> https://mklab.gr/showthread.php?tid=927 Tue, 07 Jul 2026 17:34:25 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=927 Introduction to Graph Theory 
By (author): Khee Meng Koh 


Summary

Introduction to Graph Theory: With Solutions to Selected Problems is a comprehensive introduction to the fascinating world of graph theory, a branch of mathematics that studies networks and relationships through abstract structures called graphs. The book develops the fundamental concepts of graph theory, including vertices, edges, connectivity, paths, cycles, trees, graph coloring, and related topics, while emphasizing both theoretical understanding and problem-solving skills. Designed as an accessible resource for students and learners, it combines clear explanations with carefully selected exercises and solutions that help readers build intuition and apply mathematical techniques to a wide range of problems.

Beyond presenting the basic foundations of graph theory, the book highlights how these ideas form the language behind many modern applications, from computer science and algorithms to communication networks, optimization, and data analysis. By connecting abstract mathematical reasoning with practical problem-solving, it shows why graphs have become one of the most powerful tools for understanding complex systems. This work serves not only as an educational introduction but also as a gateway into deeper areas of combinatorics and discrete mathematics, demonstrating the lasting importance of graph theory in both pure mathematics and real-world applications. 

BOOK]]> Introduction to Graph Theory 
By (author): Khee Meng Koh 


Summary

Introduction to Graph Theory: With Solutions to Selected Problems is a comprehensive introduction to the fascinating world of graph theory, a branch of mathematics that studies networks and relationships through abstract structures called graphs. The book develops the fundamental concepts of graph theory, including vertices, edges, connectivity, paths, cycles, trees, graph coloring, and related topics, while emphasizing both theoretical understanding and problem-solving skills. Designed as an accessible resource for students and learners, it combines clear explanations with carefully selected exercises and solutions that help readers build intuition and apply mathematical techniques to a wide range of problems.

Beyond presenting the basic foundations of graph theory, the book highlights how these ideas form the language behind many modern applications, from computer science and algorithms to communication networks, optimization, and data analysis. By connecting abstract mathematical reasoning with practical problem-solving, it shows why graphs have become one of the most powerful tools for understanding complex systems. This work serves not only as an educational introduction but also as a gateway into deeper areas of combinatorics and discrete mathematics, demonstrating the lasting importance of graph theory in both pure mathematics and real-world applications. 

BOOK]]> https://mklab.gr/showthread.php?tid=522 Sun, 21 Jun 2026 13:10:14 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=522 Dots and Lines 
by [Antony Bonato]

Summary 

Dots and Lines: Hidden Networks in Social Media, AI, and Nature by Anthony Bonato explores how the simple mathematical idea of networks—dots (nodes) connected by lines (edges)—can reveal hidden structures in the modern world. 
The book introduces network science through accessible examples from social media, artificial intelligence, Bitcoin, politics, biology, climate systems, and human relationships, showing how connections between objects can explain complex phenomena.
 Bonato demonstrates that networks are everywhere, from the spread of memes and information online to neural connections and natural systems, offering readers an engaging view of how graph theory helps us understand technology, society, and nature. 

BOOK PAGE]]> Dots and Lines 
by [Antony Bonato]

Summary 

Dots and Lines: Hidden Networks in Social Media, AI, and Nature by Anthony Bonato explores how the simple mathematical idea of networks—dots (nodes) connected by lines (edges)—can reveal hidden structures in the modern world. 
The book introduces network science through accessible examples from social media, artificial intelligence, Bitcoin, politics, biology, climate systems, and human relationships, showing how connections between objects can explain complex phenomena.
 Bonato demonstrates that networks are everywhere, from the spread of memes and information online to neural connections and natural systems, offering readers an engaging view of how graph theory helps us understand technology, society, and nature. 

BOOK PAGE]]>