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The line graphs of trees are exactly the claw-free block graphs. [22] These graphs have been used to solve a problem in extremal graph theory, of constructing a graph with a given number of edges and vertices whose largest tree induced as a subgraph is as small as possible. [23] All eigenvalues of the adjacency matrix A of a line graph are at ...
A best-fit line chart (simple linear regression) A parody line graph (1919) by William Addison Dwiggins. Charts often include an overlaid mathematical function depicting the best-fit trend of the scattered data. This layer is referred to as a best-fit layer and the graph containing this layer is often referred to as a line graph.
An arc diagram is a style of graph drawing, in which the vertices of a graph are placed along a line in the Euclidean plane, with edges being drawn as semicircles in one or both of the two halfplanes bounded by the line, or as smooth curves formed by sequences of semicircles. In some cases, line segments of the line itself are also allowed as ...
A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph. [2] In the abstract, all that matters is which pairs of vertices are connected by edges.
Paths are often important in their role as subgraphs of other graphs, in which case they are called paths in that graph. A path is a particularly simple example of a tree, and in fact the paths are exactly the trees in which no vertex has degree 3 or more. A disjoint union of paths is called a linear forest.
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.
Let V be a vector space of dimension n over a field F (with n≥2), and let Hom(V,V) denote the linear transformations on V.An n-trace diagram is a graph = (,), where the sets V i (i = 1, 2, n) are composed of vertices of degree i, together with the following additional structures:
GeoGebra is a dynamic geometry program that can be used to create geometric objects free-hand using compass-and-ruler tools. It can also be used to plot implicit curves, parametric curves, and loci of points. It supports SVG, PNG, EPS, PDF, EMF, PGF/TikZ and PSTricks as export formats and has support for LaTeX formulas within text objects.