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The definition of global minimum point also proceeds similarly. If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x ∗, if there exists some ε > 0 such that f(x ∗) ≥ f(x) for all x in X within distance ε of x ∗.
The stationary points are the red circles. In this graph, they are all relative maxima or relative minima. The blue squares are inflection points.. In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.
A saddle point (in red) on the graph of z = x 2 − y 2 (hyperbolic paraboloid). In mathematics, a saddle point or minimax point [1] is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. [2]
Euclidean minimum spanning tree ⊆ relative neighborhood graph ⊆ Urquhart graph ⊆ Gabriel graph ⊆ Delaunay triangulation. [ 18 ] [ 19 ] Another graph guaranteed to contain the minimum spanning tree is the Yao graph , determined for points in the plane by dividing the plane around each point into six 60° wedges and connecting each point ...
The minimum degree of a graph is denoted by (), and is the minimum of 's vertices' degrees. In the multigraph shown on the right, the maximum degree is 5 and the minimum degree is 0. In a regular graph, every vertex has the same degree, and so we can speak of the degree of the graph.
A planar graph and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. [1]
The Gilbert–Varshamov bound is the best known in terms of relative distance for codes over alphabets of size less than 49. [ citation needed ] For larger alphabets, algebraic geometry codes sometimes achieve an asymptotically better rate vs. distance tradeoff than is given by the Gilbert–Varshamov bound.
The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local maximum. Otherwise, a cubic function is monotonic. The graph of a cubic function is symmetric with respect to its inflection point; that is, it is invariant under a rotation of a half turn around this point.