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Everything about Polyhedral graph
Graph made from vertices and edges of a convex polyhedron
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. The analogue concept for polytopes of general dimension are the polytopal graphs. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Polyhedral graphA 5-minute orientation
- Skim a recent paper: Analytical railway line capacity methods from graph-theoretical and polyhedral perspectivesInfluential work since 2022
- Pick up a classic book: Unobstructed shortest paths in polyhedral environmentsThe most-reprinted book on the subject
- Read the landmark paper: Computing the aspect graph for line drawings of polyhedral objectsCited 102 times
- Go sideways: Herschel graphA closely related topic
- Go sideways: Barnette's conjectureA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Computing the aspect graph for line drawings of polyhedral objects
Set covering and packing formulations of graph coloring: Algorithms and first polyhedral results
A polyhedral graph theory approach to revenue management in the airline industry
Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfaces
A Polyhedral Approach for Graph Coloring1
Polyhedral groups and graph amalgamation products
Graph-theoretical analysis of the bonding topology in polyhedral organic cations
A Graph Theoretic Approach to Strong Monotonicity with respect to Polyhedral Cones
🆕 Influential since 2022
Analytical railway line capacity methods from graph-theoretical and polyhedral perspectives
Shellability of Polyhedral Joins of Simplicial Complexes and Its Application to Graph Theory
Independence numbers of polyhedral graphs
Automorphism Groups in Polyhedral Graphs
On polyhedral graphs and their complements
đź“š Books worth reading
Unobstructed shortest paths in polyhedral environmentsVarol Akman · 1987
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Herschel graph In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the…
- Barnette's conjecture Unsolved problem in mathematics Is every cubic bipartite polyhedral graph Hamiltonian? More unsolved problems in mathematics Barnette's conjecture is an…
- Barnette–Bosák–Lederberg graph In the mathematical field of graph theory, the Barnette–Bosák–Lederberg graph is a cubic (that is, 3-regular) polyhedral graph with no Hamiltonian cycle…
- Tutte graph In the mathematical field of graph theory, the Tutte graph is a 3-regular graph with 46 vertices and 69 edges named after W. T. Tutte. It has chromatic…
- Goldner–Harary graph In the mathematical field of graph theory, the Goldner–Harary graph is a simple undirected graph with 11 vertices and 27 edges. It is named after Anita…
- Steinitz's theorem In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices…
- Tutte embedding In graph drawing and geometric graph theory, a Tutte embedding or barycentric embedding of a simple, 3-vertex-connected, planar graph is a crossing-free…
- Tait's conjecture In mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle (along the edges) through all its vertices"…