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In mathematics, the term linear is used in two distinct senses for two different properties: . linearity of a function (or mapping);; linearity of a polynomial.; An example of a linear function is the function defined by () = (,) that maps the real line to a line in the Euclidean plane R 2 that passes through the origin.
Graphic representation of a minute fraction of the WWW, demonstrating hyperlinks.. Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
Layered graph drawing or hierarchical graph drawing is a type of graph drawing in which the vertices of a directed graph are drawn in horizontal rows or layers with the edges generally directed downwards. [1] [2] [3] It is also known as Sugiyama-style graph drawing after Kozo Sugiyama, who first developed this drawing style. [4]
A path graph or linear graph of order n ≥ 2 is a graph in which the vertices can be listed in an order v 1, v 2, …, v n such that the edges are the {v i, v i+1} where i = 1, 2, …, n − 1. Path graphs can be characterized as connected graphs in which the degree of all but two vertices is 2 and the degree of the two remaining vertices is 1.
For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. [3] [4] In category theory, a map may refer to a morphism. [2] The term transformation can be used interchangeably, [2] but transformation often refers to a function from a set to itself.
SL – special linear group. SO – special orthogonal group. SOC – second order condition. Soln – solution. Sp – symplectic group. Sp – trace of a matrix, from the German "spur" used for the trace. sp, span – linear span of a set of vectors. (Also written with angle brackets.) Spec – spectrum of a ring. Spin – spin group.
A queue layout of a given graph is defined by a total ordering of the vertices of the graph together with a partition of the edges into a number of "queues". The set of edges in each queue is required to avoid edges that are properly nested: if ab and cd are two edges in the same queue, then it should not be possible to have a < c < d < b in the vertex ordering.
A variable often used to denote a graph, especially when another graph has already been denoted by G. H-coloring An H-coloring of a graph G (where H is also a graph) is a homomorphism from H to G. H-free A graph is H-free if it does not have an induced subgraph isomorphic to H, that is, if H is a forbidden induced subgraph.