Hamming graph (original) (raw)
Les graphes de Hamming forment une famille de graphes. Le graphe de Hamming de dimension d sur un alphabet de taille q est défini de la manière suivante : est le graphe dont les sommets sont , l'ensemble des mots de longueur sur un alphabet , où . Deux sommets sont adjacents dans s'ils sont à une distance de Hamming de 1, c'est-à-dire si leurs étiquettes ne diffèrent que d'un symbole.
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| dbo:abstract | 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 S be a set of q elements and d a positive integer. The Hamming graph H(d,q) has vertex set Sd, the set of ordered d-tuples of elements of S, or sequences of length d from S. Two vertices are adjacent if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph H(d,q) is, equivalently, the Cartesian product of d complete graphs Kq. 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 H(d,q), the graphs in this more general class are not necessarily distance-regular, but they continue to be regular and vertex-transitive. (en) Les graphes de Hamming forment une famille de graphes. Le graphe de Hamming de dimension d sur un alphabet de taille q est défini de la manière suivante : est le graphe dont les sommets sont , l'ensemble des mots de longueur sur un alphabet , où . Deux sommets sont adjacents dans s'ils sont à une distance de Hamming de 1, c'est-à-dire si leurs étiquettes ne diffèrent que d'un symbole. (fr) Графы Хэмминга — это специальный класс графов, названных именем Ричарда Хэмминга и используемых в некоторых областях математики и информатики. (ru) Графи Геммінга — це спеціальний клас графів, названих ім'ям Річарда Геммінга, які використовуються в деяких галузях математики та інформатики. (uk) |
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| dbp:id | HammingGraph (en) |
| dbp:name | Hamming graph (en) |
| dbp:namesake | dbr:Richard_Hamming |
| dbp:properties | dbr:Vertex-transitive_graph dbr:Distance-regular_graph -regular (en) |
| dbp:title | Hamming Graph (en) |
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| rdfs:comment | Les graphes de Hamming forment une famille de graphes. Le graphe de Hamming de dimension d sur un alphabet de taille q est défini de la manière suivante : est le graphe dont les sommets sont , l'ensemble des mots de longueur sur un alphabet , où . Deux sommets sont adjacents dans s'ils sont à une distance de Hamming de 1, c'est-à-dire si leurs étiquettes ne diffèrent que d'un symbole. (fr) Графы Хэмминга — это специальный класс графов, названных именем Ричарда Хэмминга и используемых в некоторых областях математики и информатики. (ru) Графи Геммінга — це спеціальний клас графів, названих ім'ям Річарда Геммінга, які використовуються в деяких галузях математики та інформатики. (uk) 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 S be a set of q elements and d a positive integer. The Hamming graph H(d,q) has vertex set Sd, the set of ordered d-tuples of elements of S, or sequences of length d from S. Two vertices are adjacent if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph H(d,q) is, equivalently, the Cartesian product of d complete graphs Kq. (en) |
| rdfs:label | Hamming graph (en) Graphe de Hamming (fr) Граф Хэмминга (ru) Граф Геммінга (uk) |
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