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Aug 22, 2024 · Platonic Graph. A polyhedral graph corresponding to the skeleton of a Platonic solid. The five platonic graphs, the tetrahedral graph, cubical graph, octahedral graph, dodecahedral graph, and icosahedral graph, are illustrated above. They are special cases of Schlegel graphs.
- Graceful
A graceful graph is a graph that can be gracefully labeled....
- Octahedral Graph
"The" octahedral graph is the 6-node 12-edge Platonic graph...
- Icosahedral Graph
The icosahedral graph is the Platonic graph whose nodes have...
- Cubical Graph
The cubical graph is the Platonic graph corresponding to the...
- Cubic
Cubic graphs, also called trivalent graphs, are graphs all...
- Platonic Solid
The Platonic solids, also called the regular solids or...
- Dodecahedral Graph
The dodecahedral graph is the Platonic graph corresponding...
- Schlegel Graph
References Gardner, M. Wheels, Life, and Other Mathematical...
- Graceful
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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.
lecture-notes. 5.4 Polyhedral Graphs and the Platonic Solids. Regular Polygons. In this section we will see how Euler’s formula – unquestionably the most im-portant theorem about planar graphs – can help us understand polyhedra and a special family of polyhedra called the Platonic solids.
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Lecture 34: Polytopes and Platonic Solids. A half-space of R3 is the set of all points satisfying the inequality ax + by + cz d for prescribed constants a; b; c; d 2 R. For instance, the set f(x; y; z) 2 R3 j z 1g is a half-space (observe that the inequality z 1 is equivalent to 0x+0y +( 1)z 1).
Jan 24, 2023 · Definition. The Platonic graphs are a set of graphs representing the edges and vertices of the five Platonic solids.
Apr 27, 2015 · Platonic graph: A 3-connected planar graph with faces bounded by the same number of edges and vertices having the same number of incident edges. (remark: the faces of a 3-connected planar graph are well-defined due to Whitney's theorem)
What is a Planar Graph ? Definition : A planar graph is an undirected graph that can be drawn on a plane without any edges crossing. Such a drawing is called a planar representation of the graph in the plane. Ex: is a planar graph
