science

Table of vertex-symmetric digraphs

Table of vertex-symmetric digraphs 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 Table of vertex-symmetric digraphs rather than just read about it. In short: The best known vertex transitive digraphs (as of October 2008) in the directed Degree diameter problem are tabulated below. Table of the orders of the largest known vertex-symmetric graphs for the directed degree diameter problem The footnotes in the table indicate the origin of the digraph that achieves the given number of vertices: References Kautz, W.H.

Key takeaways

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

Reference excerpt

The best known vertex transitive digraphs (as of October 2008) in the directed Degree diameter problem are tabulated below.

Table of the orders of the largest known vertex-symmetric graphs for the directed degree diameter problem

The footnotes in the table indicate the origin of the digraph that achieves the given number of vertices:

References Kautz, W.H. (1969), "Design of optimal interconnection networks for multiprocessors", Architecture and Design of Digital Computers, Nato Advanced Summer Institute: 249–272 Faber, V.; Moore, J.W. (1988), "High-degree low-diameter interconnection networks with vertex symmetry:the directed case", Technical Report LA-UR-88-1051, los Alamos National Laboratory J. Dinneen, Michael; Hafner, Paul R. (1994), "New Results for the Degree/Diameter Problem", Networks, 24 (7): 359–367, arXiv:math/9504214, doi:10.1002/net.3230240702 Comellas, F.; Fiol, M.A. (1995), "Vertex-symmetric digraphs with small diameter", Discrete Applied Mathematics, 58 (1): 1–12, doi:10.1016/0166-218X(93)E0145-O Miller, Mirka; Širáň, Jozef (2005), "Moore graphs and beyond: A survey of the degree/diameter problem" (PDF), Electronic Journal of Combinatorics, Dynamic, survey D, archived from the original (PDF) on 2012-01-18, retrieved 2008-10-13 Loz, Eyal; Širáň, Jozef (2008), "New record graphs in the degree-diameter problem" (PDF), Australasian Journal of Combinatorics, 41: 63–80

External links Vertex-symmetric Digraphs online table. The Degree - Diameter Problem on CombinatoricsWiki.org. Eyal Loz's Degree-Diameter problem page.

Worked examples

Example 1 — a first encounter with Table of vertex-symmetric digraphs

Start with the simplest possible case. Write down what Table of vertex-symmetric digraphs 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 Table of vertex-symmetric digraphs 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 Table of vertex-symmetric digraphs 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 Table of vertex-symmetric digraphs

In research: Table of vertex-symmetric digraphs 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 Table of vertex-symmetric digraphs 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: Table of vertex-symmetric digraphs is common in secondary-school and first-year university syllabi. It links to neighbouring topics Directed graphs, so understanding it makes those chapters shorter.
In everyday life: Look for Table of vertex-symmetric digraphs 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 Table of vertex-symmetric digraphs in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Table of vertex-symmetric digraphs 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 Table of vertex-symmetric digraphs out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Table of vertex-symmetric digraphs in simple terms?

The best known vertex transitive digraphs (as of October 2008) in the directed Degree diameter problem are tabulated below. Table of the orders of the largest known vertex-symmetric graphs for the directed degree diameter problem The footnotes in the table indicate the origin of the digraph that ac…

Why does Table of vertex-symmetric digraphs 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 Table of vertex-symmetric digraphs?

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 Table of vertex-symmetric digraphs.