Sentence examples for vertices from inspiring English sources

The first few iterations of its Cayley graph are shown in Figure 12, where \(\{a, b\}\) is the set of generators and a right horizontal move between adjacent vertices represents composition with \(a\), an upward vertical move represents composition with \(b\), and leftward and downward moves represent composition with the inverse of \(a\) and the inverse of \(b\) respectively.

A few did so, but they extracted different features of the icons the number of vertices, say, or some linear abstraction of its shape.

Apart from being more spherical than the old 18-panel leather ball, the 32 panels of pentagons and hexagons (60 vertices and 90 edges all together) provide more seams which, like the dimples on a golfball, help "trip" the air flowing over it.

The carbonyl ligands in the tetracarbonylnickel molecule project toward the vertices of a tetrahedron, and thus the structure is referred to as tetrahedral.

Ceva's theorem, in geometry, theorem concerning the vertices and sides of a triangle.

The icosahedron itself has 20 triangular faces; when its vertices are sliced off, the triangles become hexagons.

Give \ u\) and \ v\) different colours, say red and white, as in Figure 18. Figure 18 By the inductive assumption, we may colour each of the smaller graphs with the three colours so that no edge joins vertices of the same colour, keeping fixed the colours of \ u\) and \ v\).

Moreover, it is easy to show that the Cayley graph of a generated group with word metric is quasi-isometric to a geodesic space.[1] A triangle with vertices \(x\), \ y\), \ z\) in this space is the union of three geodesic segments, between \(x\) and \ y\), between \ y\) and \ z\), and between \ z\) and \(x\).

A short induction shows that every polygon can be triangulated, i.e., non-crossing edges between non-adjacent vertices ("diagonals") can be added so that the polygon is entirely composed of non-overlapping triangles.

Regarded as a subject or "consciousness", from its perspective a point or object now corresponds to what was originally an appearance of an object, that is, a triple of numbers summing to 1; and, analogously, any coordinate system \(S'\) (that is, another subject or "consciousness") corresponds to three such triples determined by the vertices of a nondegenerate triangle.

A trajectory \((f_{n})_{n\in N}\) is a sequence of weights of vertices, such that the vertices carrying \(f_{n}\) and \(f_{n+1}\) are connected by an edge.