Graphpad prism graphs10/2/2023 An Atlas of Graphs, Oxford, England: Oxford University Press, 2004 reprint, Chapter 6 special graphs pp. If these two removed edges are replaced by two crossed edges, the result is a non-planar graph called a Möbius ladder. If the two cycles of a prism graph are broken by the removal of a single edge in the same position in both cycles, the result is a ladder graph. Other vertex-transitive polyhedral graphs include the Archimedean graphs. Other infinite sequences of polyhedral graph formed in a similar way from polyhedra with regular-polygon bases include the antiprism graphs (graphs of antiprisms) and wheel graphs (graphs of pyramids). The triangular prism and cube graph have treewidth exactly three, but all larger prism graphs have treewidth four. The pentagonal prism is one of the forbidden minors for the graphs of treewidth three. They form one of the few known infinite families of cubic partial cubes, and (except for four sporadic examples) the only vertex-transitive cubic partial cubes. 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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