Lesson plan
Hamming graph
{{Infobox graph | name = Hamming graph | namesake = Richard Hamming | vertices = | edges = \frac{d(q-1)q^d}{2} | diameter = | spectrum = \{(d (q - 1) - q i)^{\binom{d}{i} (q - 1)^i}; i = 0, \ldots, d\} | properties = -regular Vertex-transitive Distance-regular Distance-balanced Polytopal | notation = }} Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science. Let be a set of elements and a positive integer. The Hamming graph has vertex set , the set of ordered -tuples of elements of , or sequences of length from . Two vertices are adjacent if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph is, equivalently, the Cartesian product of complete graphs . In some cases, Hamming graphs may be considered more generally as the Cartesian products of complete graphs that may be of varying sizes. Unlike the Hamming graphs , the graphs in this more general class are not necessarily distance-regular, but they continue to be regular and vertex-transitive.
Article summary
{{Infobox graph | name = Hamming graph | namesake = Richard Hamming | vertices = | edges = \frac{d(q-1)q^d}{2} | diameter = | spectrum = \{(d (q - 1) - q i)^{\binom{d}{i} (q - 1)^i}; i = 0, \ldots, d\} | properties = -regular Vertex-transitive Distance-regular Distance-balanced Polytopal | notation = }} Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science. Let be a set of elements and a positive integer. The Hamming graph has vertex set , the set of ordered -tuples of elements of , or sequences of length from . Two vertices are adjacent if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph is, equivalently, the Cartesian product of complete graphs . In some cases, Hamming graphs may be considered more generally as the Cartesian products of complete graphs that may be of varying sizes. Unlike the Hamming graphs , the graphs in this more general class are not necessarily distance-regular, but they continue to be regular and vertex-transitive.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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