What is a cubic graph called?
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 bicubic graph is a cubic bipartite graph.
How to sketch a cubic graph?
In order to use a cubic graph to solve an equation:
- Find the given value on the y -axis.
- Draw a straight horizontal line across the curve.
- Draw a straight vertical line from the curve to the x -axis.
- Read off the value on the x -axis.
How do you graph a cubic function?
How do you shift a cubic function to the right?
- When by either f (x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.
- In general, a vertical stretch is given by the equation y=bf (x) y = b f ( x ) .
- In general, a horizontal stretch is given by the equation y=f (cx) y = f ( c x ) .
How to find a cubic function from its graph?
Find Cubic Function y = ax³ + bx² + cx + d. ← Enter (x,y) pairs. If you have four distinct points in the xy-plane, and no two x-coordinates are equal, then there is a unique cubic equation of the form. y = ax³ + bx² + cx + d. that passes through the four points.
Is a cubic graph a parabola?
Their graphs are parabolas. To find the x-intercepts we have to solve a quadratic equation. The vertex of a parabola is a maximum of minimum of the function. Then four points not in a line nor in a parabola determine a cubic function.
What is a cubic function graph?
A cubic function is a polynomial function of degree 3. So the graph of a cube function may have a maximum of 3 roots. i.e., it may intersect the x-axis at a maximum of 3 points. Since complex roots always occur in pairs, a cubic function always has either 1 or 3 real zeros. It cannot have 2 real zeros.
What is a square root graph called?
A radical function contains a radical expression with the independent variable (usually x) in the radicand. Usually radical equations where the radical is a square root is called square root functions. An example of a radical function would be. y=√x. This is the parent square root function and its graph looks like.
What is a cubic model?
A Cubic Model uses a cubic functions (of the form a x 3 + b x 2 + c x + d ) to model real-world situations. They can be used to model three-dimensional objects to allow you to identify a missing dimension or explore the result of changes to one or more dimensions.
How do you find the equation of a cubic graph?
If a cubic graph has three x-intercepts then it is possible to quickly express the equation in factored form. The leading coefficient can be deter...
How do you translate a cubic function?
A translation of the standard cubic function, y=x^3, takes the form y=a(x-h)^3+k. The constant h is a horizontal translation to the right, and k i...
What is the equation for a cubic function?
The equation of a cubic function can always be expressed in the standard form y=ax^3+bx^2+cx+d, where a, b, c, d are constants, with a non-zero.
How do you graph a cubic function?
In many cases, a cubic function is most easily graphed by creating a table of values and plotting the points. If the equation can be factored, it i...
The Equation of a Cubic Function
The equations of cubic functions can always be expressed in the standard form
X-Intercepts and Y-Intercepts
The points where a graph crosses the horizontal and vertical axes are called {eq}x {/eq}-intercepts and {eq}y {/eq}-intercepts. These make great reference points when graphing a function, and conversely, recognizing them in a graph can help us to identify the function's equation.
Constants
The exact shape of a cubic function is completely determined from the values of the constants {eq}a, b, c, d {/eq} in its standard form equation. Two of these constants tell us particularly useful information about the shape of the graph.
What is a cubic equation?
A cubic equation contains only terms up to and including (x^3). Here are some examples of cubic equations: [y = x^3] [y = x^3 + 5] Cubic graphs are curved but can have more than one change of direction.
What are the most common graphs?
The most commonly occurring graphs are quadratic, cubic, reciprocal, exponential and circle graphs. Their equations can be used to plot their shape. Part of. Maths.
Overview
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 bicubic graph is a cubic bipartite graph.
Symmetry
In 1932, Ronald M. Foster began collecting examples of cubic symmetric graphs, forming the start of the Foster census. Many well-known individual graphs are cubic and symmetric, including the utility graph, the Petersen graph, the Heawood graph, the Möbius–Kantor graph, the Pappus graph, the Desargues graph, the Nauru graph, the Coxeter graph, the Tutte–Coxeter graph, the Dyck graph, the Foster graph and the Biggs–Smith graph. W. T. Tutte classified the symmetric cubic graphs by …
Coloring and independent sets
According to Brooks' theorem every connected cubic graph other than the complete graph K4 can be colored with at most three colors. Therefore, every connected cubic graph other than K4 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.
According to Vizing's theorem every cubic graph needs either three or four colors for an edge col…
Topology and geometry
Cubic graphs arise naturally in topology in several ways. For example, if one considers a graph to be a 1-dimensional CW complex, cubic graphs are generic in that most 1-cell attaching maps are disjoint from the 0-skeleton of the graph. Cubic graphs are also formed as the graphs of simple polyhedra in three dimensions, polyhedra such as the regular dodecahedron with the property tha…
Hamiltonicity
There has been much research on Hamiltonicity of cubic graphs. In 1880, P.G. Tait conjectured that every cubic polyhedral graph has a Hamiltonian circuit. William Thomas Tutte provided a counter-example to Tait's conjecture, the 46-vertex Tutte graph, in 1946. In 1971, Tutte conjectured that all bicubic graphs are Hamiltonian. However, Joseph Horton provided a counterexample on 96 vertices, the Horton graph. Later, Mark Ellingham constructed two more counterexamples: the Elli…
Other properties
The pathwidth of any n-vertex cubic graph is at most n/6. The best known lower bound on the pathwidth of cubic graphs is 0.082n. It is not known how to reduce this gap between this lower bound and the n/6 upper bound.
It follows from the handshaking lemma, proven by Leonhard Euler in 1736 as part of the first paper on graph theory, that every cubic graph has an even number of vertices.
Algorithms and complexity
Several researchers have studied the complexity of exponential time algorithms restricted to cubic graphs. For instance, by applying dynamic programming to a path decomposition of the graph, Fomin and Høie showed how to find their maximum independent sets in time 2 . The travelling salesman problem in cubic graphs can be solved in time O(1.2312 ) and polynomial space.
Several important graph optimization problems are APX hard, meaning that, although they have a…
See also
• Table of simple cubic graphs