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If y 2 = x 3 − x − 1, then the field C(x, y) is an elliptic function field. The element x is not uniquely determined; the field can also be regarded, for instance, as an extension of C(y). The algebraic curve corresponding to the function field is simply the set of points (x, y) in C 2 satisfying y 2 = x 3 − x − 1.
The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.
It has book thickness 3, chromatic number 4, chromatic index 8, girth 3, radius 2, diameter 2 and is a 3-edge-connected graph. It is also a 3-tree, and therefore it has treewidth 3. Like any k-tree, it is a chordal graph. As a planar 3-tree, it forms an example of an Apollonian network.
"x^y = y^x - commuting powers". Arithmetical and Analytical Puzzles. Torsten Sillke. Archived from the original on 2015-12-28. dborkovitz (2012-01-29). "Parametric Graph of x^y=y^x". GeoGebra. OEIS sequence A073084 (Decimal expansion of −x, where x is the negative solution to the equation 2^x = x^2)
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
The cusps of order 3/2 are on the cubic curve, while the cusps of order 5/2 are on the x-axis (the tangent line at the inflection point). For the second type, consider the curve y = x 3 {\displaystyle y=x^{3}} .
In graph theory, an area of mathematics, common graphs belong to a branch of extremal graph theory concerning inequalities in homomorphism densities.Roughly speaking, is a common graph if it "commonly" appears as a subgraph, in a sense that the total number of copies of in any graph and its complement ¯ is a large fraction of all possible copies of on the same vertices.
ΔY- and YΔ-transformations are a tool both in pure graph theory as well as applications. Both operations preserve a number of natural topological properties of graphs. . For example, applying a YΔ-transformation to a 3-vertex of a planar graph, or a ΔY-transformation to a triangular face of a planar graph, results again in a planar graph.