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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 ...
The characteristic equation of a third-order constant coefficients or Cauchy–Euler (equidimensional variable coefficients) linear differential equation or difference equation is a cubic equation. Intersection points of cubic Bézier curve and straight line can be computed using direct cubic equation representing Bézier curve.
In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation F ( x , y , z ) = 0 {\displaystyle F(x,y,z)=0} applied to homogeneous coordinates ( x : y : z ) {\displaystyle (x:y:z)} for the projective plane ; or the inhomogeneous version for the affine space determined by setting z = 1 in such an ...
The Petersen graph is a cubic graph. The complete bipartite graph, is an example of a bicubic graph. In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs.
A cubic (but not bridgeless) graph with no perfect matching, showing that the bridgeless condition in Petersen's theorem cannot be omitted. In the mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows: Petersen's Theorem.
Roughly speaking, each vertex represents a 3-jm symbol, the graph is converted to a digraph by assigning signs to the angular momentum quantum numbers j, the vertices are labelled with a handedness representing the order of the three j (of the three edges) in the 3-jm symbol, and the graph represents a sum over the product of all these numbers ...
Tucker cubic (cubic K011 in the Catalogue) of triangle ABC drawn using the GeoGebra command Cubic(A,B,C,11). GeoGebra, the software package for interactive geometry, algebra, statistics and calculus application has a built-in tool for drawing the cubics listed in the Catalogue. [3] The command Cubic( <Point>, <Point>, <Point>, n)
The line graphs of cubic graphs are 4-regular and have a Hamiltonian decomposition if and only if the underlying cubic graph has a Hamiltonian cycle. [ 12 ] [ 13 ] As a consequence, Hamiltonian decomposition remains NP-complete for classes of graphs that include line graphs of hard instances of the Hamiltonian cycle problem .