Graph families | Planar graphs | Triangulation (geometry) | Perfect graphs

Apollonian network

In combinatorial mathematics, an Apollonian network is an undirected graph formed by a process of recursively subdividing a triangle into three smaller triangles. Apollonian networks may equivalently be defined as the planar 3-trees, the maximal planar chordal graphs, the uniquely 4-colorable planar graphs, and the graphs of stacked polytopes. They are named after Apollonius of Perga, who studied a related circle-packing construction. (Wikipedia).

Apollonian network
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Related pages

Graphs and Combinatorics | Stacked polytope | Connectivity (graph theory) | Perfect matching | Planar graph | Discrete Mathematics (journal) | Circle packing theorem | Polyhedral graph | Barycentric subdivision | Pentagonal prism | Problem of Apollonius | Simplicial polytope | Ternary tree | Chordal graph | Rational number | Combinatorics | W. T. Tutte | Degree (graph theory) | Kleetope | Equilateral triangle | Polyhedral combinatorics | Incenter | Clique (graph theory) | Graph theory | Goldner–Harary graph | Complete bipartite graph | Extremal graph theory | Graph minor | Loop subdivision surface | Complete graph | Polyhedron | Power law | Cubic graph | Euclidean plane | Steinitz's theorem | Biconnected component | Graph isomorphism | Partial k-tree | Forbidden graph characterization | Graph coloring | Vertex connectivity | K-tree | Four color theorem | Bridge (graph theory) | Independent set (graph theory) | Uniquely colorable graph | Bisection | Journal of Combinatorial Theory | Degeneracy (graph theory) | Apollonius of Perga | Y-Δ transform | Octahedron | Graph embedding | Graph toughness | Centroid | Apollonian gasket | Generating function | Clique-sum | Robertson–Seymour theorem