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The graph of any cubic function is similar to such a curve. The graph of a cubic function is a cubic curve, though many cubic curves are not graphs of functions. Although cubic functions depend on four parameters, their graph can have only very few shapes. In fact, the graph of a cubic function is always similar to the graph of a function of ...
Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis at y = 0).The case shown has two critical points.Here the function is () = (+) = (+) (+) and therefore the three real roots are 2, −1 and −4.
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 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. This leaves the other graphs in the 3-connected class because each 3-regular graph can be ...
Quadratic function: Second degree polynomial, graph is a parabola. Cubic function: Third degree polynomial. Quartic function: Fourth degree polynomial. Quintic function: Fifth degree polynomial. Rational functions: A ratio of two polynomials. nth root. Square root: Yields a number whose square is the given one. Cube root: Yields a number whose ...
The volume of a geometric cube is the cube of its side length, giving rise to the name. The inverse operation that consists of finding a number whose cube is n is called extracting the cube root of n. It determines the side of the cube of a given volume. It is also n raised to the one-third power. The graph of the cube function is known as the ...
The Lucas cubic is the locus of a point X such that the cevian triangle of X is the pedal triangle of some point; the point lies on the Darboux cubic. The Lucas cubic passes through the centroid, orthocenter, Gergonne point, Nagel point, de Longchamps point, other triangle centers, the vertices of the anticomplementary triangle, and the foci of ...
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.