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

Dispersion of light throughprism diagram

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Rectangularprism diagram

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HexagonalPrism diagram

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The prism graph is the line graph of the complete bipartite graph . The prism graph is isomorphic with the cubical graph. The -prism graph is isomorphic to the Haar graph .

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 , , ..., .

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Triangularprism diagram

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The prism graph is equivalent to the Cayley graph of the dihedral group with respect to the generating set (Biggs 1993, p. 126).

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

is isomorphic to the graph Cartesian product , where is the path graph on two nodes and is the cycle graph on nodes. As a result, it is a unit-distance graph (Horvat and Pisanski 2010).

Glassprism diagram

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