edge space and vertex space of an undirected graph are vector spaces defined in terms of the edge and vertex sets, respectively. These vector spaces make...

all the edges connected to the vertex. The cut surface is the vertex figure (a plane figure). This is perhaps the most common approach, and the most...

triangulated form. vertex A position (usually in 3D space) along with other information such as color, normal vector and texture coordinates. edge A connection...

directed graph, is a vertex with no incoming edges (in-degree equals 0). space In algebraic graph theory, several vector spaces over the binary field...

from the Greek téssara (τέσσαρα 'four') and aktís (ἀκτίς 'ray'), referring to the four edges from each vertex to other vertices. Hinton originally spelled...

vertices forming an edge are said to be the endpoints of this edge, and the edge is said to be incident to the vertices. A vertex w is said to be adjacent...

the convex icosahedron: A group polytopes that share both a vertex arrangement and an edge arrangement are called a regiment. 4-polytopes can also have...

borders at a vertex. Its value in radians is the length of the circular arc on the unit sphere resulting from centrally projecting one edge of the tetrahedron...

from vertex ui to vertex uj, and 0 when there is no edge. The diagonal elements of the matrix are all 0, since edges from a vertex to itself (loops) are...

each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only...

an undirected graph. Each vertex belongs to exactly one connected component, as does each edge. A graph is connected if and only if it has exactly one...

the cycle space), which consists of the edge sets that have even degree at every vertex; it forms a vector space over the two-element field. By Veblen's...

tetrahedral cells with 20 meeting at each vertex. Together they form 1200 triangular faces, 720 edges, and 120 vertices. It is the 4-dimensional analogue...

type {p}, and regular vertex figure {q}. A vertex figure (of a polyhedron) is a polygon, seen by connecting those vertices which are one edge away from...

example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its...

between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common...

represent the vertices and edges. An implementation suggested by Guido van Rossum uses a hash table to associate each vertex in a graph with an array...

(the edges of a graph are connected to every vertex without crossing other edges), and 3-connected (whenever a graph with more than three vertices, and two...

tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that, for every pair of flags, there...

is an edge-to-edge filling of the hyperbolic plane, with regular polygons as faces; these are vertex-transitive (transitive on its vertices), and isogonal...

z-depth and alpha value) of a pixel. A vertex shader is called for each vertex in a primitive (possibly after tessellation); thus one vertex in, one (updated)...

regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent...

of edges is a set of edges of which no two have a vertex in common. It is usually called a matching. A vertex coloring is a partition of the vertex set...

equivalent to a vertex coloring of the line graph L(G), the graph that has a vertex for every edge of G and an edge for every pair of adjacent edges in G. A proper...

by adding a fifth vertex one edge length distant from all the vertices of the tetrahedron. This cannot be done in 3-dimensional space. The regular 5-cell...

is an edge from the vertex x to the vertex y; neighbors(G, x): lists all vertices y such that there is an edge from the vertex x to the vertex y; add_vertex(G...

dimension: vertices have rank 0, edges rank 1 and so on. Incident faces of different ranks, for example, a vertex F of an edge G, are ordered by the relation...

intersection of half-spaces results in a polytope in vertex-representation, follows: The bounded intersection of closed half-spaces of R n {\displaystyle...

paths from the same starting vertex to the same ending vertex. Oriented trees or polytrees are DAGs formed by orienting the edges of trees (connected, acyclic...

simplices and the edges as one-dimensional simplices. The chain complex of this topological space consists of its edge space and vertex space (the Boolean...