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2. Girth (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Girth_(graph_theory)

   In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. [1] If the graph does not contain any cycles (that is, it is a forest), its girth is defined to be infinity. [2] For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3.

3. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).

4. Table of the largest known graphs of a given diameter and ...

   en.wikipedia.org/wiki/Table_of_the_largest_known...

   Below is the table of the vertex numbers for the best-known graphs (as of June 2024) in the undirected degree diameter problem for graphs of degree at most 3 ≤ d ≤ 16 and diameter 2 ≤ k ≤ 10. Only a few of the graphs in this table (marked in bold) are known to be optimal (that is, largest possible).

5. Graph (discrete mathematics) - Wikipedia

   en.wikipedia.org/wiki/Graph_(discrete_mathematics)

   In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points ) and each of the related pairs of vertices is called an edge (also called link or line ...

6. Independent set (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Independent_set_(graph_theory)

   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 ...

7. Cut (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Cut_(graph_theory)

   If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t belongs to the set T. In an unweighted undirected graph, the size or weight of a cut is the number of edges crossing the cut. In a weighted graph, the value or weight is defined by the sum of the weights of the edges crossing the ...

8. Zarankiewicz problem - Wikipedia

   en.wikipedia.org/wiki/Zarankiewicz_problem

   A bipartite graph with 4 vertices on each side, 13 edges, and no , subgraph, and an equivalent set of 13 points in a 4 × 4 grid, showing that (;).. The number (;) asks for the maximum number of edges in a bipartite graph with vertices on each side that has no 4-cycle (its girth is six or more).

9. Diameter (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Diameter_(graph_theory)

   Only finitely many Moore graphs exist, but their exact number is unknown. They provide the solutions to the degree diameter problem for their degree and diameter. [2] Small-world networks are a class of graphs with low diameter, modeling the real-world phenomenon of six degrees of separation in social networks. [3]