河內圖：修订间差异

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2022年7月26日 (二) 01:08的版本

在图论和娛樂數學，河內圖是一種無向圖，它的頂點代表河內塔謎題的可能狀態，而它的邊代表兩個狀態間，可行的移動。

此謎題包含一堆不同大小的圓盤，放置杆上的圓盤，依照愈下面愈大的順序。謎題對應 $n$ 圓盤在 $k$ 根杆上的河內圖，記做 $H_{k}^{n}$ 。^[1]^[2]每一個狀況表示每一個杆子上的圓盤，所以每一個河內圖有 $k^{n}$ 頂點。^[2]

^ Hinz, Andreas M.; Klavžar, Sandi; Petr, Ciril, 2.3 Hanoi Graphs, The tower of Hanoi—myths and maths 2nd, Cham: Birkhäuser: 120, 2018, ISBN 978-3-319-73778-2, MR 3791459, doi:10.1007/978-3-319-73779-9
^ Imrich, Wilfried; Klavžar, Sandi; Rall, Douglas F., 2.2 Hanoi Graphs, Topics in Graph Theory: Graphs and their Cartesian Product, Wellesley, MA: A K Peters: 13–15, 2008, ISBN 978-1-56881-429-2, MR 2468851

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 ==參考文獻==
 {{Reflist}}
+<ref name=hkp>{{citation
+ | last1 = Hinz | first1 = Andreas M.
+ | last2 = Klavžar | first2 = Sandi | author2-link = Sandi Klavžar
+ | last3 = Petr | first3 = Ciril
+ | contribution = 2.3 Hanoi Graphs
+ | doi = 10.1007/978-3-319-73779-9
+ | edition = 2nd
+ | isbn = 978-3-319-73778-2
+ | location = Cham
+ | mr = 3791459
+ | page = 120
+ | publisher = Birkhäuser
+ | title = The tower of Hanoi—myths and maths
+ | title-link = The Tower of Hanoi – Myths and Maths
+ | year = 2018}}</ref>
+<ref name=ikr>{{citation
+ | last1 = Imrich | first1 = Wilfried | author1-link = Wilfried Imrich
+ | last2 = Klavžar | first2 = Sandi | author2-link = Sandi Klavžar
+ | last3 = Rall | first3 = Douglas F.
+ | contribution = 2.2 Hanoi Graphs
+ | isbn = 978-1-56881-429-2
+ | location = Wellesley, MA
+ | mr = 2468851
+ | pages = 13–15
+ | publisher = A K Peters
+ | title = Topics in Graph Theory: Graphs and their Cartesian Product
+ | year = 2008}}</ref>