Search results
Results from the WOW.Com Content Network
The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices is 1, 2, 5, 19, ... (sequence A002851 in the OEIS).A classification according to edge connectivity is made as follows: the 1-connected and 2-connected graphs are defined as usual.
According to Brooks' theorem every connected cubic graph other than the complete graph K 4 has a vertex coloring with at most three colors. Therefore, every connected cubic graph other than K 4 has an independent set of at least n/3 vertices, where n is the number of vertices in the graph: for instance, the largest color class in a 3-coloring has at least this many vertices.
The points T 1, T 2, and T 3 (in red) are the intersections of the (dotted) tangent lines to the graph at these points with the graph itself. They are collinear too. The tangent lines to the graph of a cubic function at three collinear points intercept the cubic again at collinear points. [4] This can be seen as follows.
For solving the cubic equation x 3 + m 2 x = n where n > 0, Omar Khayyám constructed the parabola y = x 2 /m, the circle that has as a diameter the line segment [0, n/m 2] on the positive x-axis, and a vertical line through the point where the circle and the parabola intersect above the x-axis.
Singular cubic y 2 = x 2 ⋅ (x + 1). A parametrization is given by t ↦ (t 2 – 1, t ⋅ (t 2 – 1)). A cubic curve may have a singular point, in which case it has a parametrization in terms of a projective line. Otherwise a non-singular cubic curve is known to have nine points of inflection, over an algebraically closed field such as the ...
An ordered pair of vertices, such as an edge in a directed graph. An arrow (x, y) has a tail x, a head y, and a direction from x to y; y is said to be the direct successor to x and x the direct predecessor to y. The arrow (y, x) is the inverted arrow of the arrow (x, y). articulation point A vertex in a connected graph whose removal would ...
The graph Q 0 consists of a single vertex, while Q 1 is the complete graph on two vertices. Q 2 is a cycle of length 4. The graph Q 3 is the 1-skeleton of a cube and is a planar graph with eight vertices and twelve edges. The graph Q 4 is the Levi graph of the Möbius configuration. It is also the knight's graph for a toroidal chessboard.
cubic graph special points: Image title: Graph showing the relationship between the roots, turning or stationary points and inflection point of a cubic polynomial and its first and second derivatives by CMG Lee. The vertical scale is compressed 1:50 relative to the horizontal scale for ease of viewing.