A camel graph is a graph formed by all possible moves of a hypothetical chess piece called a "camel" which moves analogously to a knight except that it is
restricted to moves that change by one square along one axis of the board and three
squares along the other. To form the graph, each chessboard square is considered
a vertex, and vertices connected by allowable camel moves are considered edges. It
is therefore a -leaper graph. The term is used by Jelliss (2019), who
notes, "The first purely camel tour I know of is that by T. R. Dawson in 'Caissa's
Playthings' in Cheltenham Examiner 1913, where he used the name."

Ball and Coxeter (1987, p. 186) state, "Euler's method [to construct a Hamiltonian cycle] can be applied to find routes
of this kind: for instance, he applied it to find a re-entrant route by which a piece
that moved two cells forward like a castle [rook] and then one cell like a bishop
would occupy in succession all the black cells on the board." Such a series
of moves corresponds to a camel tour (Jelliss 2019).

Like bishop graphs, camel graph are disconnected (except for the trivial singleton graph on a board which is trivially connected), with each component
being restricted to either black or white squares. Again, as with the bishop
graph, the black and white components of an camel graph are isomorphic iff and are not both odd.

The camel graph consists of a connected
white component and a disconnected black component which, as in the case of the knight
graph, includes a central (unreachable from all of the other squares) isolated
vertex.

Camel graphs are bicolorable, bipartite, class 1, perfect, triangle-free, and weakly perfect.

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

Ball, W. W. R. and Coxeter, H. S. M. Mathematical
Recreations and Essays, 13th ed. New York: Dover, 1987.Dawson,
T. R. "CaissaÕs Playthings." Cheltenham Examiner. 1913.Dawson,
T. R. L'Echiquier. 1928.Hansson, F. Problem 715 in Problemist
Fairy Chess Supplement. April and June 1933.Jelliss, G. "The
Big Beasts: Camel 1,
3Shaped Boards." §10.27 in Knight's
Tour Notes. 2019. http://www.mayhematics.com/p/KTN10_Leapers.pdfKraitchik,
M. Le Problème du Cavalier. 1927.