![]() ![]() The n-gonal prism graphs for even values of n are partial cubes. It can be generated by two elements, a rotation by an angle of 2 π/ n and a single reflection, and its Cayley graph with this generating set is the prism graph. The order- n dihedral group is the group of symmetries of a regular n-gon in the plane it acts on the n-gon by rotations and reflections. Īs with many vertex-transitive graphs, the prism graphs may also be constructed as Cayley graphs. ![]() They may also be constructed as the Cartesian product of a cycle graph with a single edge. Prism graphs are examples of generalized Petersen graphs, with parameters GP( n,1). Octagonal prism graph – 16 vertices, 24 edgesĪlthough geometrically the star polygons also form the faces of a different sequence of (self-intersecting and non-convex) prismatic polyhedra, the graphs of these star prisms are isomorphic to the prism graphs, and do not form a separate sequence of graphs.Heptagonal prism graph – 14 vertices, 21 edges.Hexagonal prism graph – 12 vertices, 18 edges.Pentagonal prism graph – 10 vertices, 15 edges.Triangular prism graph – 6 vertices, 9 edges.The individual graphs may be named after the associated solid: In the mathematical field of graph theory, a prism graph is a graph that has one of the prisms as its skeleton. ![]()
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