Search results
Results from the WOW.Com Content Network
Template talk: Hamiltonian platonic graphs.svg. ... Download as PDF; Printable version ... This template does not require a rating on Wikipedia's content assessment ...
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Donate
Hamiltonian platonic graphs: Image title: Orthographic projections and planar graphs of Hamiltonian cycles of the vertices of the five Platonic solids by CMG Lee. Only the octahedron has an Eulerian path, made by extending the Hamiltonian path with the dotted path. Width: 100%: Height: 100%
The polyhedral graph formed as the Schlegel diagram of a regular dodecahedron. In geometric graph theory, a branch of mathematics, a polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron. Alternatively, in purely graph-theoretic terms, the polyhedral graphs are the 3-vertex-connected, planar graphs.
For degree two, any odd cycle is such a graph, and for degree three, four, and five, these graphs can be constructed from platonic solids by replacing a single edge by a path of two adjacent edges. In Vizing's planar graph conjecture , Vizing (1965) states that all simple, planar graphs with maximum degree six or seven are of class one, closing ...
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.In particular, all its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves regular polytopes of dimension j≤ n.
The graph of a regular octahedron The skeleton of a regular octahedron can be represented as a graph according to Steinitz's theorem , provided the graph is planar —its edges of a graph are connected to every vertex without crossing other edges—and 3-connected graph —its edges remain connected whenever two of more three vertices of a ...
The web graph W 4,2 is a cube. The web graph W n,r is a graph consisting of r concentric copies of the cycle graph C n, with corresponding vertices connected by "spokes". Thus W n,1 is the same graph as C n, and W n,2 is a prism. A web graph has also been defined as a prism graph Y n+1, 3, with the edges of the outer cycle removed. [7] [10]