Circle Graph Formula

Circle Graph Formula

The circle graph, or pie chart, is one of the most common graphs used to represent real-world information using circles, spheres, and angular data. Data and information are visualized using it. In a Circle Graph Formula, a circle with a 360-degree angle at its centre is divided into different parts with different angles. Each of these smaller parts is called an arc, and the angles of these arcs determine their names.

What is Circle Graph Formula?

One uses circle graphs whenever some data needs to be represented visually as a fraction. To display the percentage of the total, Circle Graph Formula or pie charts are used. Comparing the areas perfectly helps determine why one is smaller/greater than the other.

Therefore, pie charts are better suited to data sets with a limited number of buckets.

Solved Examples of Circle Graph Formula

Here are the Circle Graph Formula.

Category percentage = (Amount in the Category / Total) × 100

Category angle = (Amount in Category ⁄ Total) × 360°

Using an O(n 2)-time algorithm, Spinrad (1994) tests whether a given undirected graph has n vertex pairs and constructs chords that represent it if it does.

Other NP-complete problems can be solved in polynomial time when restricted to circle graphs. In O(n 3 ) time, Kloks (1996) showed how to determine the tree width of a Circle Graph Formula and construct an optimal tree decomposition. A minimum fill-in (a chordal graph containing the given circle graph as a subgraph) may also be found in O(n 3).

A circle graph’s chromatic number is the minimum number of colours that can be used to colour its chords so that no two crossing chords share the same colour. The chromatic number of a Circle Graph Formula can be arbitrarily large because arbitrarily large sets of chords can cross each other, and determining the chromatic number of a circle graph is NP-complete. The problem of colouring a Circle Graph Formula with four colours remains NP-complete. According to Unger (1992), finding a colouring with three colours is polynomial time. However, his description of the result omits many details. In the case of triangle-free circle graphs (that is, when k = 3) the chromatic number is at most five, which is tight: it is possible to colour triangle-free circle graphs with five colours, and triangle-free circle graphs with five colours exist.

It is possible to colour a Circle Graph Formula with at most three colours if it has girth at least five (i.e. there are no triangles and no four-vertex cycles). Square graphs that are triangle-free can be coloured in the same way as square graphs that are represented as Cartesian products of trees; in this correspondence, the number of colours corresponds to the number of trees in the representation of the product.

A circle graph is an abstract representation of two-terminal switch box wiring in VLSI physical design. There are two-terminal nets in this case, and the terminals are placed on the perimeter of the rectangle. There is no doubt that the intersection graph of these nets is a circle graph.  Different nets must be arranged in different conducting layers to ensure that they remain electrically disconnected. This routing problem can therefore be represented by circle graphs in a variety of ways. A graph is a Circle Graph Formula if and only if it is the overlap graph of a set of intervals on a line. The vertices of the graph correspond to the intervals, and two vertices are connected by an edge if the two intervals overlap, but neither contains the other.

A Circle Graph Formula is a special case of string graphs, which are intersection graphs of curves in the plane.

Distance-hereditary graphs, permutation graphs, and difference graphs are all circle graphs. Circle graphs are also outer planar graphs.

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