science

McLaughlin graph

McLaughlin graph is a science 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 McLaughlin graph rather than just read about it. In short: In the mathematical field of graph theory, the McLaughlin graph is a strongly regular graph with parameters (275, 112, 30, 56) and is the only such graph. The group theorist Jack McLaughlin discovered that the automorphism group of this graph had a subgroup of index 2 which was a previously undiscovered finite simple group, now called the McLaughlin sporadic group.

Key takeaways

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

Reference excerpt

In the mathematical field of graph theory, the McLaughlin graph is a strongly regular graph with parameters (275, 112, 30, 56) and is the only such graph. The group theorist Jack McLaughlin discovered that the automorphism group of this graph had a subgroup of index 2 which was a previously undiscovered finite simple group, now called the McLaughlin sporadic group. The automorphism group has rank 3, meaning that its point stabilizer subgroup divides the remaining 274 vertices into two orbits. Those orbits contain 112 and 162 vertices. The former is the colinearity graph of the generalized quadrangle GQ(3,9). The latter is a strongly regular graph called the local McLaughlin graph.

References McLaughlin, Jack (1969), "A simple group of order 898,128,000", in Brauer, R.; Sah, Chih-han (eds.), Theory of Finite Groups (Symposium, Harvard Univ., Cambridge, Mass., 1968), Benjamin, New York, pp. 109–111, MR 0242941

External links Andries Brouwer. "McLaughlin graph".

Worked examples

Example 1 — a first encounter with McLaughlin graph

Start with the simplest possible case. Write down what McLaughlin graph claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 McLaughlin graph 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 McLaughlin graph 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 McLaughlin graph

In research: McLaughlin graph appears in science 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 McLaughlin graph 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: McLaughlin graph is common in secondary-school and first-year university syllabi. It links to neighbouring topics Graph theory stubs, Individual graphs, Regular graphs, so understanding it makes those chapters shorter.
In everyday life: Look for McLaughlin graph 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 McLaughlin graph in 20 minutes

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

Frequently asked questions

What is McLaughlin graph in simple terms?

Why does McLaughlin graph matter?

Because it connects several science 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 McLaughlin graph?

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 McLaughlin graph.