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["Antelope", m, n].

REFERENCES

Jelliss, G. "The Big Beasts: Antelope 3, 4." §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.