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The latter may occur even if the distance in the other direction between the same two vertices is defined. In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path ...
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y. Distance-transitive graphs were first defined in 1971 by Norman L. Biggs and ...
A time–distance diagram is a chart with two axes: one for time, the other for location. The units on either axis depend on the type of project: time can be expressed in minutes (for overnight construction of railroad modification projects such as the installation of switches) or years (for large construction projects); the location can be (kilo)meters, or other distinct units (such as ...
The geometric-distance matrix is a different type of distance matrix that is based on the graph-theoretical distance matrix of a molecule to represent and graph the 3-D molecule structure. [8] The geometric-distance matrix of a molecular structure G is a real symmetric n x n matrix defined in the same way as a 2-D matrix.
Where the terminology may be ambiguous, the graphs in which non-edges must be a non-unit distance apart may be called strict unit distance graphs [3] or faithful unit distance graphs. [2] The subgraphs of unit distance graphs are equivalently the graphs that can be drawn in the plane using only one edge length. [ 4 ]
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
Every even power of a distance-hereditary graph G (that is, the graph G 2i formed by connecting pairs of vertices at distance at most 2i in G) is a chordal graph. [10] Every distance-hereditary graph can be represented as the intersection graph of chords on a circle, forming a circle graph. This can be seen by building up the graph by adding ...
Signed distance functions are applied, for example, in real-time rendering, [7] for instance the method of SDF ray marching, and computer vision. [8] [9] SDF has been used to describe object geometry in real-time rendering, usually in a raymarching context, starting in the mid 2000s.