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A metric space defined over a set of points in terms of distances in a graph defined over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected. The eccentricity ϵ(v) of a vertex v is the greatest distance between v and any other vertex; in ...
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 ...
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
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 ...
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.
This graph is distance regular with intersection array {7,4,1;1,2,7} and automorphism group PGL(2,7). Some first examples of distance-regular graphs include: The complete graphs. The cycle graphs. The odd graphs. The Moore graphs. The collinearity graph of a regular near polygon. The Wells graph and the Sylvester graph.
Travel-time curve is a graph showing the relationship between the distance from the epicenter to the observation point and the travel time. [2] [3] Travel-time curve is drawn when the vertical axis of the graph is the travel time and the horizontal axis is the epicenter distance of each observation point. [4] [5] [6]
A fan graph is a graph on n + 1 vertices where there is an edge between vertex i and n + 1 for all i = 1, 2, 3, …, n, and there is an edge between vertex i and i + 1 for all i = 1, 2, 3, …, n – 1. The resistance distance between vertex n + 1 and vertex i ∈ {1, 2, 3, …, n} is +