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5. A chord of a circle is a line segment connecting two points on the circle; the intersection graph of a collection of chords is called a circle graph. chromatic Having to do with coloring; see color. Chromatic graph theory is the theory of graph coloring. The chromatic number χ(G) is the minimum number of colors needed in a proper coloring of G.
An example of how intersecting sets define a graph. In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets.Any graph can be represented as an intersection graph, but some important special classes of graphs can be defined by the types of sets that are used to form an intersection representation of them.
Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs. [ 17 ]
Every graph can be represented as an intersection graph in this way. [11] The intersection number of the graph is the smallest number k {\displaystyle k} such that there exists a representation of this type for which the union of the sets in F {\displaystyle {\mathcal {F}}} has k {\displaystyle k} elements. [ 1 ]
In graph theory, a branch of mathematics, a map graph is an undirected graph formed as the intersection graph of finitely many simply connected and internally disjoint regions of the Euclidean plane. The map graphs include the planar graphs , but are more general.
Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are ...
In graph theory, a string graph is an intersection graph of curves in the plane; each curve is called a "string".Given a graph G, G is a string graph if and only if there exists a set of curves, or strings, such that the graph having a vertex for each curve and an edge for each intersecting pair of curves is isomorphic to G.