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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.
An intersection graph is a graph whose vertices correspond to sets or geometric objects, with an edge between two vertices exactly when the corresponding two sets or objects have a nonempty intersection. Several classes of graphs may be defined as the intersection graphs of certain types of objects, for instance chordal graphs (intersection ...
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
A gear graph, denoted G n, is a graph obtained by inserting an extra vertex between each pair of adjacent vertices on the perimeter of a wheel graph W n. Thus, G n has 2n+1 vertices and 3n edges. [4] Gear graphs are examples of squaregraphs, and play a key role in the forbidden graph characterization of squaregraphs. [5]
In graph theory, particularly in the theory of hypergraphs, the line graph of a hypergraph H, denoted L(H), is the graph whose vertex set is the set of the hyperedges of H, with two vertices adjacent in L(H) when their corresponding hyperedges have a nonempty intersection in H. In other words, L(H) is the intersection graph of a family of ...
Intersections of the unaccented modern Greek, Latin, and Cyrillic scripts, considering only the shapes of the letters and ignoring their pronunciation Example of an intersection with sets The intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B {\displaystyle A\cap B} , [ 3 ] is the set of all objects that ...
When restricted to graphs with maximum degree 3, it can be solved in time O(1.0836 n). [10] For many classes of graphs, a maximum weight independent set may be found in polynomial time. Famous examples are claw-free graphs, [11] P 5-free graphs [12] and perfect graphs. [13] For chordal graphs, a maximum weight independent set can be found in ...
This category contains articles about classes of graphs defined or characterized by intersection representations. See graph families for information on more classes of graphs. Pages in category "Intersection classes of graphs"