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A typical example of a homogeneous function of degree k is the function defined by a homogeneous polynomial of degree k. The rational function defined by the quotient of two homogeneous polynomials is a homogeneous function; its degree is the difference of the degrees of the numerator and the denominator; its cone of definition is the linear ...
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 grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt".
From the handshaking lemma, a k-regular graph with odd k has an even number of vertices. A theorem by Nash-Williams says that every k ‑regular graph on 2k + 1 vertices has a Hamiltonian cycle. Let A be the adjacency matrix of a graph. Then the graph is regular if and only if = (, …,) is an eigenvector of A. [2]
We ask: When are two graphs the same? (i.e., graph isomorphism) The graphs in question may be expressed differently in terms of graph equations. [1] What are the graphs G and H such that the line graph of G is same as the total graph of H? (What are G and H such that L(G) = T(H) ?). For example, G = K 3, and H = K 2 are the solutions of the ...
Whether they're moving out of the house they've been in for 30 years or are first-time homeowners who are eager to kickoff homeownership. Help them make their move feel extra special with a ...
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