A fiveleaper graph is a graph formed by all possible moves of a hypothetical chess piece called a "fiveleaper" 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 or by five squares along one axis.
To form the graph, each chessboard square is considered a vertex, and vertices connected
by allowable fiveleaper moves are considered edges. The fiveleaper gets its name
from the fact that all its move have a length of 5 squares.

The fiveleaper is similar to the hypothetical chess piece called an "antelope," but it can make an antelope's move or a rook's move of exactly 5 squares.

The plots above show the graphs corresponding to antelope graphs on chessboards for to 7.

The
fiveleaper graph is connected for (trivially) and , Hamiltonian for
(trivially) and 8, 10, 12, 14, ...(and
all other even but for no odd up to at least ), and traceable for
up to at least (and likely for all larger values as well).

The
fiveleaper graph is connected for , Hamiltonian for
(trivially) and even (up to least and likely all larger values), and traceable
for
(up to at least
and likely for all larger values as well).

Precomputed properties of fiveleaper graphs are implemented in the Wolfram Language as GraphData["Fiveleaper", m, n].