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The 13 distinct cubic distance-regular graphs are K 4 (or Tetrahedral graph), K 3,3, the Petersen graph, the Cubical graph, the Heawood graph, the Pappus graph, the Coxeter graph, the Tutte–Coxeter graph, the Dodecahedral graph, the Desargues graph, Tutte 12-cage, the Biggs–Smith graph, and the Foster graph.
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 ...
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 ...
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 ...
Unlike a regular distance-time graph, the distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a way that an object moving at the speed of light is depicted as following a 45° angle to the diagram's axes.
Click on a date/time to view the file as it appeared at that time. Date/Time Thumbnail Dimensions User Comment; current: ... Distance (graph theory) Metadata.
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 ...
Other specific graphs that are unit distance graphs include the Petersen graph, [10] the Heawood graph, [11] the wheel graph (the only wheel graph that is a unit distance graph), [3] and the Moser spindle and Golomb graph (small 4-chromatic unit distance graphs). [12]