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...

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...

cubic bipartite polyhedral graph Hamiltonian? More unsolved problems in mathematics Barnette's conjecture is an unsolved problem in graph theory, a branch...

In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices...

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

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...

Umpei; Hyugaji, Sachiko (1994), "Topological twin graphs. Smallest pair of isospectral polyhedral graphs with eight vertices", Journal of Chemical Information...

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

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...

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

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...

cubic polyhedral graphs are Hamiltonian. Grinberg's theorem is named after Latvian mathematician Emanuel Grinberg, who proved it in 1968. A planar graph is...

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...

adjacency matrix of the vertices representing the polyhedral graph of the unit-radius 120-cell, the graph diameter is 15, connecting each vertex to its coordinate-negation...

In the mathematical field of graph theory, the 26-fullerene graph is a polyhedral graph with V = 26 vertices and E = 39 edges. Its planar embedding has...

polyhedral (and therefore by necessity also 3-vertex-connected, vertex-transitive, and planar graphs), and also Hamiltonian graphs. The first graph in...

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,...

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...

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...

Franklin graph Frucht graph Goldner–Harary graph Golomb graph Grötzsch graph Harries graph Harries–Wong graph Herschel graph Hoffman graph Holt graph Horton...

graph theory, the Barnette–Bosák–Lederberg graph is a cubic (that is, 3-regular) polyhedral graph with no Hamiltonian cycle, the smallest such graph possible...

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...

approach. Force-directed methods in graph drawing date back to the work of Tutte (1963), who showed that polyhedral graphs may be drawn in the plane with all...

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...

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...

between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. General cuboids have many different...

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...

represented as a polyhedral graph, meaning a planar graph (one that can be drawn without crossing edges) and 3-vertex-connected graph (remaining connected...

solid figure or to its boundary surface. The terms solid polyhedron and polyhedral surface are commonly used to distinguish the two concepts. Also, the term...

The Goldner–Harary graph is also non-Hamiltonian. The smallest possible number of vertices for a non-Hamiltonian polyhedral graph is 11. Therefore, the...