# Vertices

### Some articles on vertices:

Features of Collaboration Graphs
... Thus people who never co-authored a joint paper represent isolated vertices in the collaboration graph of mathematicians ... were shown to have "small world topology" they have a very large number of vertices, most of small degree, that are highly clustered, and a "giant" connected component with small average ...
Schönhardt Polyhedron - Impossibility of Triangulation
... to partition the Schönhardt polyhedron into tetrahedra whose vertices are vertices of the polyhedron ... there is no tetrahedron that lies entirely inside the Schönhardt polyhedron and has vertices of the polyhedron as its four vertices ... For, among any four vertices of the Schönhardt polyhedron, at least one pair of vertices from these four vertices must be a diagonal of the polyhedron, which lies entirely outside the polyhedron ...
Hemi-octahedron
... It has 4 triangular faces, 6 edges, and 3 vertices ... that there are two distinct edges between every pair of vertices – any two vertices define a digon ...
Simplex Graph
... G is itself a graph, with one node for each clique (a set of mutually adjacent vertices) in G ... used to form the clique graph, as is every set of one vertex and every set of two adjacent vertices ... the structure of a median algebra the median of three cliques A, B, and C is formed by the vertices that belong to a majority of the three cliques ...
Squaregraph - Related Graph Classes
... As well as being planar graphs, squaregraphs are median graphs, meaning that for every three vertices u, v, and w there is a unique median vertex m(u,v,w ... median graphs more generally, squaregraphs are also partial cubes their vertices can be labeled with binary strings such that the Hamming distance between strings is equal to the shortest ...