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cycle (graph theory)

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Cycle (graph theory)
In graph theory, two types of object are commonly called cycles. One type of cycle, more commonly called a closed walk, consists of a sequence of vertices starting and ending at the same vertex, with each two consecutive vertices in the sequence adjacent to each other in the graph. The other type of cycle, sometimes called a simple cycle, circuit, circle, or polygon, is a closed walk with no repetitions of vertices or edges allowed, other than the repetition of the starting and ending vertex. Simple cycles may also be described by their sets of edges, unlike closed walks for which the multiset of edges does not unambiguously determine the vertex ordering. A directed cycle in a directed graph is a sequence of vertices starting and ending at the same vertex such that, for each two consecutive vertices of the cycle, there exists an edge directed from the earlier vertex to the later one; the same distinction between closed walks and simple cycles may be made in the directed case.

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Cycle (théorie des graphes)
Dans un graphe non orienté, un cycle est une suite d'arêtes consécutives (chaine) dont les deux sommets extrémités sont identiques. Dans les graphes orientés, la notion équivalente est celle de circuit, même si on parle parfois aussi de cycle (par exemple dans l'expression graphe acyclique orienté).

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Polska Wikipedia – Darmowa encyklopedia

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Cykl (teoria grafów)
Rodzaje cykli
Cykl to droga (inaczej: ścieżka prosta) zamknięta, czyli taka, której koniec (ostatni wierzchołek) jest identyczny z początkiem (pierwszym wierzchołkiem).

Cykl prosty – cykl, w którym żaden wierzchołek się nie powtarza:

Cykl Hamiltona – cykl prosty przebiegający przez wszystkie wierzchołki grafu.

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Wikipedia 日本語 - フリー百科事典

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閉路(へいろ、circuit, closed walk, cycle)あるいは閉道(へいどう、closed path)とは、始点と終点が同じのこと。すなわち、出発点に戻るような辿り方のことである。グラフ理論位相幾何学において用いられる。




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