Hosoya index (original) (raw)
The Hosoya index, also known as the Z index, of a graph is the total number of matchings in it. The Hosoya index is always at least one, because the empty set of edges is counted as a matching for this purpose. Equivalently, the Hosoya index is the number of non-empty matchings plus one. The index is named after Haruo Hosoya. It is used as a topological index in chemical graph theory. Complete graphs have the largest Hosoya index for any given number of vertices; their Hosoya indices are the telephone numbers.
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| dbo:abstract | The Hosoya index, also known as the Z index, of a graph is the total number of matchings in it. The Hosoya index is always at least one, because the empty set of edges is counted as a matching for this purpose. Equivalently, the Hosoya index is the number of non-empty matchings plus one. The index is named after Haruo Hosoya. It is used as a topological index in chemical graph theory. Complete graphs have the largest Hosoya index for any given number of vertices; their Hosoya indices are the telephone numbers. (en) En théorie des graphes, l'indice de Hosoya d'un graphe, également connu sous le nom d'indice Z, est le nombre total de couplages que possède ce graphe. L'indice de Hosoya est toujours au moins égal à 1, parce que par convention l'ensemble vide d'arêtes est compté comme un couplage dans ce contexte. De manière équivalente, l'indice de Hosoya est le nombre de couplages non vides plus un. L'indice porte le nom de (en). (fr) グラフ理論における細矢インデックスまたはZインデックスとは、与えられたグラフのマッチングの総数のことである。このとき辺の空集合もマッチングの一つとして数えるので、細矢インデックスは必ず1以上である。同じことだが、「グラフの空でないマッチングの個数に1を足した値」と定義してもよい。 (ja) (Топологический) индекс Хосойи, известный также как Z индекс, графа — это полное число паросочетаний на нём. Индекс Хосойи всегда больше либо равен одному, поскольку пустое множество рёбер считается как паросочетание. Эквивалентно, индекс Хосойи — это число непустых паросочетаний плюс один. (ru) |
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| gold:hypernym | dbr:Number |
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| rdfs:comment | The Hosoya index, also known as the Z index, of a graph is the total number of matchings in it. The Hosoya index is always at least one, because the empty set of edges is counted as a matching for this purpose. Equivalently, the Hosoya index is the number of non-empty matchings plus one. The index is named after Haruo Hosoya. It is used as a topological index in chemical graph theory. Complete graphs have the largest Hosoya index for any given number of vertices; their Hosoya indices are the telephone numbers. (en) En théorie des graphes, l'indice de Hosoya d'un graphe, également connu sous le nom d'indice Z, est le nombre total de couplages que possède ce graphe. L'indice de Hosoya est toujours au moins égal à 1, parce que par convention l'ensemble vide d'arêtes est compté comme un couplage dans ce contexte. De manière équivalente, l'indice de Hosoya est le nombre de couplages non vides plus un. L'indice porte le nom de (en). (fr) グラフ理論における細矢インデックスまたはZインデックスとは、与えられたグラフのマッチングの総数のことである。このとき辺の空集合もマッチングの一つとして数えるので、細矢インデックスは必ず1以上である。同じことだが、「グラフの空でないマッチングの個数に1を足した値」と定義してもよい。 (ja) (Топологический) индекс Хосойи, известный также как Z индекс, графа — это полное число паросочетаний на нём. Индекс Хосойи всегда больше либо равен одному, поскольку пустое множество рёбер считается как паросочетание. Эквивалентно, индекс Хосойи — это число непустых паросочетаний плюс один. (ru) |
| rdfs:label | Indice de Hosoya (fr) Hosoya index (en) 細矢インデックス (ja) Индекс Хосойи (ru) |
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