These vertices form the ring of the configuration ; a configuration with k vertices in its ring is a k-ring configuration, and the configuration together with its ring is called the ringed configuration.

These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices ( singular: vertex ) or corners.

These transformations displace the triangle in the plane without changing the angle at each vertex or the distances between vertices.

These could be measured much more accurately than bearings of the vertices, which depended on a compass.

These vertices and propagators produce a single cover of the moduli space of-point closed string scattering amplitudes so no higher order vertices are required.

These algorithms require amortized O ( α ( n )) time per operation, where adding vertices and edges and determining the connected component in which a vertex falls are both operations, and α ( n ) is a very slow-growing inverse of the very quickly growing Ackermann function.

These systems may perform gradient descent based minimization of an energy function, or they may translate the forces directly into velocities or accelerations for the moving vertices.

These vertices become identified as conjugate 3-transpositions in the symmetry group Fi < sub > 22 </ sub > of the graph.

These curves may cross each other but must not touch any vertices other than their endpoints.

These chords are in turn uniquely determined by the four corresponding endpoints of the chords, which are all exterior vertices.

These are chords between adjacent exterior vertices, and form the perimeter of the polygon.

These new vertices introduced to decrease the total length of connection are known as Steiner points or Steiner vertices.

These include the forests, k-trees ( maximal graphs with a given treewidth ), split graphs ( graphs that can be partitioned into a clique and an independent set ), block graphs ( graphs in which every biconnected component is a clique ), interval graphs ( graphs in which each vertex represents an interval of a line and each edge represents a nonempty intersection between two intervals ), trivially perfect graphs ( interval graphs for nested intervals ), threshold graphs ( graphs in which two vertices are adjacent when their total weight exceeds a numerical threshold ), windmill graphs ( formed by joining equal cliques at a common vertex ), and strongly chordal graphs ( chordal graphs in which every even cycle of length six or more has an odd chord ).

These include the bipartite graphs, the chordal graphs, the comparability graphs, the distance-hereditary graphs ( in which shortest path distances in connected induced subgraphs equal those in the whole graph ), and the wheel graphs that have an odd number of vertices.

These include vertices, edges, faces, polygons and surfaces.

These 2-faces play the same role as the vertices where arrangements of triangles meet in a triangulation of a 2-manifold, which is easier to visualize.

These arguments allowed to show that certain measurables of loop-erased random walk are ( in the limit ) conformally invariant, and that the expected number of vertices in a loop-erased random walk stopped at a circle of radius r is of the order of.

These are the vertices of a subgraph, the U < sub > 3 </ sub >( 3 ) graph.

These vertices then undergo transformation and per-vertex lighting.

These are set on a graph, a set of connected vertices.

These are just another couple of characters to roll.

These men are not callous.

These things are important to almost all Persians and perhaps most important to the most ordinary.

These are traversed by another line of vaults, and thus rooms, arched on all four sides, are formed.

These songs ( practically all Persian music, for that matter ) are limited to a range of two octaves.

These are not, however, differences in federal structure.

These my grandmother left in their places ( they are still there, more persistent and longer-lived than the generations of man ) and planted others like them, that flourished without careful tending.

These are like the initial ways in which the world forces itself upon the self and thrusts the self into decision and choice.

These are suggestive of Selma Lagerlof.

These assumptions lead to an organization with one man at the top, six directly under him, six under each of these, and so on until there are six levels of personnel.

These ways are absolutely irreconcilable because they offer two different recipes for man's redemption from chaos.

These responses are explicable in terms of characteristics inherent in the crisis.

These discoveries are of present interest chiefly to the scientific community ; ;

These are personality factors ; ;

These are, if the research is done with subtlety and skill, researchable topics, but the research is missing.

These moments are historical events in the lives of individual authors with which the student of comparative literature must be frequently concerned.

These lives are in themselves outside of the moral order and are unburdened with moral responsibility.

These conceptions and the manner in which they were transposed into poetry or engendered by poetic form are intrinsic to western life from the time of Aeschylus to that of Shakespeare.

These biographical analogies are obvious, and far too much time has been spent speculating on their possible implications.

These women whose organization grew out of the old suffrage movement are dedicated to Thomas Jefferson's dictum that one must cherish the people's spirit but `` Keep alive their attention ''.

These are, of course, the same people whose support he has only now rejected to seek the independent vote.

These are New York, Pennsylvania, Michigan, Maryland, Missouri, New Jersey, Illinois and Minnesota.

These men are spenders.