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The degree diameter problem seeks tight relations between the diameter, number of vertices, and degree of a graph. One way of formulating it is to ask for the largest graph with given bounds on its degree and diameter. For any fixed degree, this maximum size is exponential in the diameter, with the base of the exponent depending on the degree. [1]
Some instances of the smallest bounding circle. The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane.
6) defines the beam diameter as the distance between diametrically opposed points in that cross-section of a beam where the power per unit area is 1/e (0.368) times that of the peak power per unit area. This is the beam diameter definition that is used for computing the maximum permissible exposure to a laser beam.
Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2) 2. Solving for r, we find the required result.
Another generalization is to calculate the number of coprime integer solutions , to the inequality m 2 + n 2 ≤ r 2 . {\displaystyle m^{2}+n^{2}\leq r^{2}.\,} This problem is known as the primitive circle problem , as it involves searching for primitive solutions to the original circle problem. [ 9 ]
LeetCode LLC, doing business as LeetCode, is an online platform for coding interview preparation. The platform provides coding and algorithmic problems intended for users to practice coding . [ 1 ] LeetCode has gained popularity among job seekers in the software industry and coding enthusiasts as a resource for technical interviews and coding ...
The diameter d of a graph is the maximum eccentricity of any vertex in the graph. That is, d is the greatest distance between any pair of vertices or, alternatively, d = max v ∈ V ϵ ( v ) = max v ∈ V max u ∈ V d ( v , u ) . {\displaystyle d=\max _{v\in V}\epsilon (v)=\max _{v\in V}\max _{u\in V}d(v,u).}
The size of G is bounded above by the Moore bound; for 1 < k and 2 < d, only the Petersen graph, the Hoffman-Singleton graph, and possibly graphs (not yet proven to exist) of diameter k = 2 and degree d = 57 attain the Moore bound. In general, the largest degree-diameter graphs are much smaller in size than the Moore bound.