astronomy

L. W. Beineke

L. W. Beineke is a astronomy 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 L. W. Beineke rather than just read about it. In short: Lowell Wayne Beineke (born 1939) is a professor of graph theory at Purdue University Fort Wayne. He is known for his elegant characterization of line graphs (derived graph) in terms of the forbidden graph characterization.

Key takeaways

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

Reference excerpt

Lowell Wayne Beineke (born 1939) is a professor of graph theory at Purdue University Fort Wayne. He is known for his elegant characterization of line graphs (derived graph) in terms of the forbidden graph characterization. Beineke has taught mathematics at Purdue University Fort Wayne since 1965. He received a B.S. from Purdue University in 1961, an M.S. from the University of Michigan in 1962, and a Ph.D. in 1965. His Ph.D. advisor was Frank Harary. Beineke holds the Jack W. Schrey chair of mathematical sciences. He was the recipient of the Amoco Foundation Outstanding Teaching Award in 1978, and again in 1992.

Books Selected topics in graph theory, LW Beineke, R. J. Wilson, 1978, Academic Press, New York

Research work Topological graph theory, AT White, LW Beineke, Selected Topics in Graph Theory, 1978 "The thickness of the complete graph", LW Beineke, Frank Harary – Canadian Journal of Mathematics, 1965, books.google.com Tournaments, K. B. Reid, L. W. Beineke - Selected topics in graph theory, 1978 "Characterizations of derived graphs", LW Beineke – J. Combin. Theory Ser. B, 1970

References

L. W. Beineke at the Mathematics Genealogy Project Indiana University-Purdue University Fort Wayne

Worked examples

Example 1 — a first encounter with L. W. Beineke

Start with the simplest possible case. Write down what L. W. Beineke claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 L. W. Beineke 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 L. W. Beineke 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 L. W. Beineke

In research: L. W. Beineke appears in astronomy 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 L. W. Beineke 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: L. W. Beineke is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1939 births, Graph theorists, Indiana University–Purdue University Fort Wayne faculty, so understanding it makes those chapters shorter.
In everyday life: Look for L. W. Beineke 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 L. W. Beineke in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what L. W. Beineke 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 L. W. Beineke out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is L. W. Beineke in simple terms?

Why does L. W. Beineke matter?

Because it connects several astronomy 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 L. W. Beineke?

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 L. W. Beineke.