Definition & Betydelse | Engelska ordet GRAPHS

Definition av GRAPHS

1. böjningsform av graph

Exempel på hur man kan använda GRAPHS i en mening

• In contrast to the early work of Antoine-Henri Jomini, he argued that war could not be quantified or reduced to mapwork, geometry, and graphs.
• Using the probabilistic method it is easy to show that extractor graphs with really good parameters exist.
• In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
• The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length or distance of each segment.
• In graph (b) there is a perfect matching (of size 3) since all 6 vertices are matched; in graphs (a) and (c) there is a maximum-cardinality matching (of size 2) which is not perfect, since some vertices are unmatched.
• This is asymptotically the fastest known single-source shortest-path algorithm for arbitrary directed graphs with unbounded non-negative weights.
• He is a leading expert in splittings and accessibility of discrete groups, groups acting on graphs and trees, JSJ-decompositions, the topology of 3-manifolds and the structure of their fundamental groups.
• In terms of their asymptotic time complexity, these three algorithms are equally fast for sparse graphs, but slower than other more sophisticated algorithms.
• In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski.
• In 1898, he presented a counterexample to Tait's claimed theorem about 1-factorability of 3-regular graphs, which is nowadays known as the "Petersen graph".
• In computability theory, the simplest numbering scheme is the assignment of natural numbers to a set of objects such as functions, rational numbers, graphs, or words in some formal language.
• In graphs of the electronic band structure of solids, the band gap refers to the energy difference (often expressed in electronvolts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors.
• The adjacency matrix of the union of disjoint graphs (or multigraphs) is the direct sum of their adjacency matrices.
• Applications of the harmonic series and its partial sums include Euler's proof that there are infinitely many prime numbers, the analysis of the coupon collector's problem on how many random trials are needed to provide a complete range of responses, the connected components of random graphs, the block-stacking problem on how far over the edge of a table a stack of blocks can be cantilevered, and the average case analysis of the quicksort algorithm.
• Treewidth may also be defined from other structures than tree decompositions, including chordal graphs, brambles, and havens.
• Examples of combinatorial species are (finite) graphs, permutations, trees, and so on; each of these has an associated generating function which counts how many structures there are of a certain size.
• Chordless cycles may be used to characterize perfect graphs: by the strong perfect graph theorem, a graph is perfect if and only if none of its holes or antiholes have an odd number of vertices that is greater than three.
• Some of his major contributions have been on the topics of the existence of semiregular automorphisms (see group action for an explanation of this) of vertex-transitive graphs, the existence of Hamiltonian paths and cycles in vertex-transitive graphs, and the structures of semi-symmetric graphs and half-transitive graphs.
• Embedding diagrams are three dimensional graphs commonly used to educationally illustrate gravitational potential by drawing gravitational potential fields as a gravitational topography, depicting the potentials as so-called gravitational wells, sphere of influence.
• In this way, the combinatorial formulation for finite families of finite sets and the graph-theoretic formulation for finite graphs are equivalent.

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