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A circle with five chords and the corresponding circle graph. In graph theory, a circle graph is the intersection graph of a chord diagram.That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
A pie chart (or a circle chart) is a circular statistical graphic which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area ) is proportional to the quantity it represents.
If a circular-arc graph G has an arc model that leaves some point of the circle uncovered, the circle can be cut at that point and stretched to a line, which results in an interval representation. Unlike interval graphs, however, circular-arc graphs are not always perfect, as the odd chordless cycles C 5, C 7, etc., are circular-arc graphs.
Chord diagrams are conventionally visualized by arranging the objects in their order around a circle, and drawing the pairs of the matching as chords of the circle. The number of different chord diagrams that may be given for a set of 2 n {\displaystyle 2n} cyclically ordered objects is the double factorial ( 2 n − 1 ) ! ! {\displaystyle (2n ...
Circular segment - the part of the sector that remains after removing the triangle formed by the center of the circle and the two endpoints of the circular arc on the boundary. Scale of chords; Ptolemy's table of chords; Holditch's theorem, for a chord rotating in a convex closed curve; Circle graph; Exsecant and excosecant
Circular layouts are a good fit for communications network topologies such as star or ring networks, [1] and for the cyclic parts of metabolic networks. [2] For graphs with a known Hamiltonian cycle, a circular layout allows the cycle to be depicted as the circle, and in this way circular layouts form the basis of the LCF notation for Hamiltonian cubic graphs.
The line graph of a graph G is defined as the intersection graph of the edges of G, where we represent each edge as the set of its two endpoints. A string graph is the intersection graph of curves on a plane. A graph has boxicity k if it is the intersection graph of multidimensional boxes of dimension k, but not of any smaller dimension.
Bipartite graph, a graph without odd cycles (cycles with an odd number of vertices) Cactus graph, a graph in which every nontrivial biconnected component is a cycle; Cycle graph, a graph that consists of a single cycle; Chordal graph, a graph in which every induced cycle is a triangle; Directed acyclic graph, a directed graph with no directed ...