A prism graph, denoted ,
(Gallian 1987), or (Hladnik et al. 2002), and sometimes also called
a circular ladder graph and denoted (Gross and Yellen 1999, p. 14), is a graph
corresponding to the skeleton of an -prism. Prism graphs are therefore
both planar and polyhedral.
An -prism graph has nodes and edges, and is equivalent to the generalized
Petersen graph .
For odd ,
the -prism is isomorphic to the circulant
graph ,
as can be seen by rotating the inner cycle by and increasing its radius to equal that of the outer
cycle in the top embeddings above. In addition, for odd ,
is isomorphic to ,
, ..., .

Prism graphs are graceful (Gallian 1987, Frucht
and Gallian 1988, Gallian 2018).

The numbers of directed Hamiltonian paths on the -prism graph for , 4, ... are 60, 144, 260, 456, 700, 1056, 1476, ... (OEIS
A124350), which has the beautiful closed form

where
is the floor function (M. Alekseyev, pers.
comm., Feb. 7, 2008).

The numbers of graph cycles on the -prism graph for , 4, ... are 14, 28, 52, 94, 170, ... (OEIS A077265),
illustrated above for .

Biggs, N. L. Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press, 1993.Gallian,
J. "Labeling Prisms and Prism Related Graphs." Congr. Numer.59,
89-100, 1987.Gallian, J. "Dynamic Survey of Graph Labeling."
Elec. J. Combin.DS6. Dec. 21, 2018. https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6.Gross,
J. T. and Yellen, J. Graph
Theory and Its Applications. Boca Raton, FL: CRC Press, p. 14, 1999.Frucht
R.
and
Gallian, J. A. "Labeling Prisms." Ars Combin.26, 69-82, 1988.Hladnik, M.; Marušič, D.; and Pisanski, T. "Cyclic
Haar Graphs." Disc. Math.244, 137-153, 2002.Horvat,
B. and Pisanski, T. "Products of Unit Distance Graphs." Disc. Math.310,
1783-1792, 2010.Hosoya, H. and Harary, F. "On the Matching Properties
of Three Fence Graphs." J. Math. Chem.12, 211-218, 1993.Read,
R. C. and Wilson, R. J. An
Atlas of Graphs. Oxford, England: Oxford University Press, p. 263 and
270, 1998.Sloane, N. J. A. Sequences A077265
and A124350 in "The On-Line Encyclopedia
of Integer Sequences."