mathematics

Graph Theory, 1736–1936

Graph Theory, 1736–1936 is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Graph Theory, 1736–1936 rather than just read about it. In short: Graph Theory, 1736–1936 is a book in the history of mathematics on graph theory. It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the first textbook on the subject, published in 1936 by Dénes Kőnig.

Key takeaways

Graph Theory, 1736–1936 belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Graph Theory, 1736–1936 to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Graph Theory, 1736–1936 from memory before moving on to harder problems.

Reference excerpt

Graph Theory, 1736–1936 is a book in the history of mathematics on graph theory. It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the first textbook on the subject, published in 1936 by Dénes Kőnig. Graph Theory, 1736–1936 was edited by Norman L. Biggs, E. Keith Lloyd, and Robin J. Wilson, and published in 1976 by the Clarendon Press. The Oxford University Press published a paperback second edition in 1986, with a corrected reprint in 1998.

Topics Graph Theory, 1736–1936 contains copies, extracts, and translations of 37 original sources in graph theory, grouped into ten chapters and punctuated by commentary on their meaning and context. It begins with Euler's 1736 paper "Solutio problematis ad geometriam situs pertinentis" on the seven bridges of Königsberg (both in the original Latin and in English translation) and ending with Dénes Kőnig's book Theorie der endlichen und unendlichen Graphen. The source material touches on recreational mathematics, chemical graph theory, the analysis of electrical circuits, and applications of graph theory in abstract algebra. Also included are background material and portraits on the mathematicians who originally developed this material. The chapters of the book organize the material into topics within graph theory, rather than being strictly chronological. The first chapter, on paths, includes maze-solving algorithms as well as Euler's work on Euler tours. Next, a chapter on circuits includes material on knight's tours in chess (a topic that long predates Euler), Hamiltonian cycles, and the work of Thomas Kirkman on polyhedral graphs. Next follow chapters on spanning trees and Cayley's formula, chemical graph theory and graph enumeration, and planar graphs, Kuratowski's theorem, and Euler's polyhedral formula. There are three chapters on the four color theorem and graph coloring, a chapter on algebraic graph theory, and a final chapter on graph factorization. Appendices provide a brief update on graph history since 1936, biographies of the authors of the works included in the book, and a comprehensive bibliography.

Audience and reception Reviewer Ján Plesník names the book the first ever published on the history of graph theory, and although Hazel Perfect notes that parts of it can be difficult to read, Plesník states that it can also be used as "a self-contained introduction" to the field, and Edward Maziarz suggests its use as a textbook for graph theory courses. Perfect calls the book "fascinating ... full of information", thoroughly researched and carefully written, and Maziarz finds inspiring the ways in which it describes serious mathematics as arising from frivolous starting points. Fernando Q. Gouvêa calls it a "must-have" for anyone interested in graph theory, and Philip Peak also recommends it to anyone interested more generally in the history of mathematics.

References

External links Full text of first edition at the Internet Archive

Worked examples

Example 1 — a first encounter with Graph Theory, 1736–1936

Start with the simplest possible case. Write down what Graph Theory, 1736–1936 claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Graph Theory, 1736–1936 before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Graph Theory, 1736–1936 ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Graph Theory, 1736–1936

In research: Graph Theory, 1736–1936 appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Graph Theory, 1736–1936 in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Graph Theory, 1736–1936 is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1976 non-fiction books, Books about the history of mathematics, Graph theory, so understanding it makes those chapters shorter.
In everyday life: Look for Graph Theory, 1736–1936 outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Graph Theory, 1736–1936 in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Graph Theory, 1736–1936 means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Graph Theory, 1736–1936 out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Graph Theory, 1736–1936 in simple terms?

Why does Graph Theory, 1736–1936 matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Graph Theory, 1736–1936?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Graph Theory, 1736–1936.