Polyhedral graph information

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...

combinatorics Polyhedral cone Polyhedral cylinder Polyhedral convex function Polyhedral dice Polyhedral dual Polyhedral formula Polyhedral graph Polyhedral group...

Strangulated graphs are the graphs in which every peripheral cycle is a triangle. In a maximal planar graph (or more generally a polyhedral graph) the peripheral...

permutohedron Subhamiltonian graph, a subgraph of a planar Hamiltonian graph Tait's conjecture (now known false) that 3-regular polyhedral graphs are Hamiltonian Travelling...

the graph union of the 4-vertex cycle and the single-vertex graph, as reported by Collatz and Sinogowitz in 1957. The smallest pair of polyhedral cospectral...

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...

vertex, the prism graphs are vertex-transitive graphs. As polyhedral graphs, they are also 3-vertex-connected planar graphs. Every prism graph has a Hamiltonian...

dipole graph. Conversely, the dual to an n-edge dipole graph is an n-cycle. According to Steinitz's theorem, every polyhedral graph (the graph formed...

number 3, chromatic index 3, girth 4 and diameter 8. The Tutte graph is a cubic polyhedral graph, but is non-hamiltonian. Therefore, it is a counterexample...

bicubic polyhedral graph is Hamiltonian. When a cubic graph is Hamiltonian, LCF notation allows it to be represented concisely. If a cubic graph is chosen...

In graph theory, the Golomb graph is a polyhedral graph with 10 vertices and 18 edges. It is named after Solomon W. Golomb, who constructed it (with a...

plane graphs by the same   V − E + F   {\displaystyle \ V-E+F\ } formula as for polyhedral surfaces, where F is the number of faces in the graph, including...

only, ignoring higher-dimensional faces. For instance, a polyhedral graph is the polytope graph of a three-dimensional polytope. By a result of Whitney...

projective-plane embeddings of graphs with planar covers The strong Papadimitriou–Ratajczak conjecture: every polyhedral graph has a convex greedy embedding...

general mathematical language, a cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. A special case of a cuboid is a rectangular...

to at most two blocks, then it is called a Christmas cactus. Every polyhedral graph has a Christmas cactus subgraph that includes all of its vertices,...

planar graph is the skeleton of a convex polyhedron; for this reason, this class of graphs is also known as the polyhedral graphs. A Euclidean graph is a...

every polyhedral graph contains a cycle of length Ω ( n log 3 ⁡ 2 ) {\displaystyle \Omega (n^{\log _{3}2})} . The polyhedral graphs are the graphs that...

cycles in an undirected graph that together include each edge of the graph exactly twice. For instance, for any polyhedral graph, the faces of a convex...

any polyhedral graph and its dual graph can be represented by two circle packings, such that the two tangent circles representing a primal graph edge...

forms a graph with 8 vertices and 12 edges, called the cube graph. It is a special case of the hypercube graph. It is one of 5 Platonic graphs, each a...

studied over a century earlier by Kirkman. Halin graphs are polyhedral graphs, meaning that every Halin graph can be used to form the vertices and edges of...

equivalent polyhedra can be thought of as one of many embeddings of a polyhedral graph on the sphere. Unless otherwise specified, in this article (and in...