science

Minimum degree spanning tree

Minimum degree spanning tree 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 Minimum degree spanning tree rather than just read about it. In short: In graph theory, a minimum degree spanning tree is a subset of the edges of a connected graph that connects all the vertices together, without any cycles, and its maximum degree of its vertices as small as possible. That is, it is a spanning tree whose maximum degree is minimal.

Key takeaways

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

Reference excerpt

In graph theory, a minimum degree spanning tree is a subset of the edges of a connected graph that connects all the vertices together, without any cycles, and its maximum degree of its vertices as small as possible. That is, it is a spanning tree whose maximum degree is minimal. The decision problem is: Given a graph G and an integer k, does G have a spanning tree such that no vertex has degree greater than k? This is also known as the degree-constrained spanning tree problem.

Algorithms Finding the minimum degree spanning tree of an undirected graph is NP-hard. This can be shown by constructing a reduction from the Hamiltonian path problem. For directed graphs, finding the minimum degree spanning tree is also NP-hard. R. Krishman and B. Raghavachari (2001) have a quasi-polynomial time approximation algorithm to solve the problem for directed graphs. M. Haque, Md. R. Uddin, and Md. A. Kashem (2007) found a linear time algorithm that can find the minimum degree spanning tree of series-parallel graphs with small degrees. G. Yao, D. Zhu, H. Li, and S. Ma (2008) found a polynomial time algorithm that can find the minimum degree spanning tree of directed acyclic graphs.

References

Worked examples

Example 1 — a first encounter with Minimum degree spanning tree

Start with the simplest possible case. Write down what Minimum degree spanning tree 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 Minimum degree spanning tree 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 Minimum degree spanning tree 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 Minimum degree spanning tree

In research: Minimum degree spanning tree 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 Minimum degree spanning tree 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: Minimum degree spanning tree is common in secondary-school and first-year university syllabi. It links to neighbouring topics Spanning tree, so understanding it makes those chapters shorter.
In everyday life: Look for Minimum degree spanning tree 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 Minimum degree spanning tree in 20 minutes

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

Frequently asked questions

What is Minimum degree spanning tree in simple terms?

Why does Minimum degree spanning tree 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 Minimum degree spanning tree?

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 Minimum degree spanning tree.