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Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
A complete bipartite graph of K 4,7 showing that Turán's brick factory problem with 4 storage sites (yellow spots) and 7 kilns (blue spots) requires 18 crossings (red dots) For any k, K 1,k is called a star. [2] All complete bipartite graphs which are trees are stars. The graph K 1,3 is called a claw, and is used to define the claw-free graphs ...
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.
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1 . At x = 1 , the value of y equals the base because any number raised to the power of 1 is the number itself.
The points P 1, P 2, and P 3 (in blue) are collinear and belong to the graph of x 3 + 3 / 2 x 2 − 5 / 2 x + 5 / 4 . The points T 1, T 2, and T 3 (in red) are the intersections of the (dotted) tangent lines to the graph at these points with the graph itself. They are collinear too.
A graph is bipartite if and only if it is 2-colorable, (i.e. its chromatic number is less than or equal to 2). [3] A graph is bipartite if and only if every edge belongs to an odd number of bonds, minimal subsets of edges whose removal increases the number of components of the graph. [16]
The edge-connectivity for a graph with at least 2 vertices is less than or equal to the minimum degree of the graph because removing all the edges that are incident to a vertex of minimum degree will disconnect that vertex from the rest of the graph. [1] For a vertex-transitive graph of degree d, we have: 2(d + 1)/3 ≤ κ(G) ≤ λ(G) = d. [11]
Multipartite graph. In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently, it is a graph that can be colored with k colors, so that no two endpoints of an edge have the same color. When k = 2 these are the bipartite graphs, and when k = 3 ...