Antelope Graph
المؤلف:
Jelliss, G
المصدر:
"The Big Beasts: Antelope {3, 4}." §10.36 in Knights Tour Notes. 2019.
الجزء والصفحة:
...
24-2-2022
2175
Antelope Graph
An antelope graph (Jelliss 2019) is a graph formed by all possible moves of a hypothetical chess piece called an "antelope" which moves analogously to a knight except that it is restricted to moves that change by three squares along one axis of the board and four squares along the other. To form the graph, each chessboard square is considered a vertex, and vertices connected by allowable antelope moves are considered edges. It is therefore a 
-leaper graph.
The plots above show the graphs corresponding to antelope graph on 
chessboards for 
to 7.
The 
antelope graph is connected for 
, Hamiltonian for 
(trivially) and 14 (but for no odd 
or other even values 
), and traceable for 
and 21 (with the status for 
unknown and 
unknown).
Precomputed properties of antelope graphs are implemented in the Wolfram Language as GraphData[![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/AntelopeGraph/Inline12.svg" style="height:22px; width:6px" />"Antelope", ![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/AntelopeGraph/Inline13.svg" style="height:22px; width:6px" />m, n![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/AntelopeGraph/Inline14.svg" style="height:22px; width:6px" />![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/AntelopeGraph/Inline15.svg" style="height:22px; width:6px" />].
REFERENCES
Jelliss, G. "The Big Beasts: Antelope ![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/AntelopeGraph/Inline16.svg" style="height:22px; width:6px" />3, 4![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/AntelopeGraph/Inline17.svg" style="height:22px; width:6px" />." §10.36 in Knight's Tour Notes. 2019.
http://www.mayhematics.com/p/KTN10_Leapers.pdfMarlow, T. W. and Jelliss, G. P. "Fiveleaper Tours." May 2002. https://www.mayhematics.com/t/pf.htm.
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