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2. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   The size of a graph is ... For example, graph-based methods are often used to 'cluster ... One of the most famous and stimulating problems in graph theory is the ...

3. Degree diameter problem - Wikipedia

   en.wikipedia.org/wiki/Degree_diameter_problem

   The size of G is bounded above by the Moore bound; for 1 < k and 2 < d, only the Petersen graph, the Hoffman-Singleton graph, and possibly graphs (not yet proven to exist) of diameter k = 2 and degree d = 57 attain the Moore bound. In general, the largest degree-diameter graphs are much smaller in size than the Moore bound.

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 July 2022) 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. List of NP-complete problems - Wikipedia

   en.wikipedia.org/wiki/List_of_NP-complete_problems

   Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...

6. 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 ...

7. Diameter (graph theory) - Wikipedia

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

   In graph theory, the diameter of a connected undirected graph is the farthest distance between any two of its vertices. That is, it is the diameter of a set for the set of vertices of the graph, and for the shortest-path distance in the graph. Diameter may be considered either for weighted or for unweighted graphs.

8. Clique (graph theory) - Wikipedia

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

   Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science : the task of finding whether there is a clique of a given size in a graph (the clique problem ) is NP-complete , but despite this hardness result, many algorithms ...

9. 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.