查看“︁河內圖”︁的源代码

{{Expert needed|subject=數學|time=2022-07-26T03:40:42+00:00}}
[[File:Hanoi-Graph-7.svg|thumb|一個<math>H^7_3</math>的河內圖]]
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。

==建構==
[[File:Sierpinski Pascal triangle.svg|thumb|一個<math>H^5_3</math>的河內圖 (黑色圓圈) 由[[楊輝三角形]]推得]]
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<math>n</math>圓盤在<math>k</math>根杆上的河內圖，記做<math>H^n_k</math>。{{r|hkp|ikr}}每一個狀態表示每一個杆子上的圓盤，所以每一個河內圖有<math>k^n</math>頂點。{{r|ikr}}

==參考文獻==
{{Reflist|refs=

<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>

}}

[[Category:平面图]]