# Category: Strongly regular graphs

Berlekamp–Van Lint–Seidel graph
In graph theory, the Berlekamp–Van Lint–Seidel graph is a locally linear strongly regular graph with parameters . This means that it has 243 vertices, 22 edges per vertex (for a total of 2673 edges),
Clebsch graph
In the mathematical field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with 80 edges. The 80-edge gra
Rook's graph
In graph theory, a rook's graph is a graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's graph represents a square on a chessboard, and each edge con
Brouwer–Haemers graph
In the mathematical field of graph theory, the Brouwer–Haemers graph is a 20-regular undirected graph with 81 vertices and 810 edges.It is a strongly regular graph, a distance-transitive graph, and a
Paley graph
In mathematics, Paley graphs are dense undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ by a quadratic residue. The Paley graphs fo
Gewirtz graph
The Gewirtz graph is a strongly regular graph with 56 vertices and valency 10. It is named after the mathematician Allan Gewirtz, who described the graph in his dissertation.
Shrikhande graph
In the mathematical field of graph theory, the Shrikhande graph is a named graph discovered by S. S. Shrikhande in 1959. It is a strongly regular graph with 16 vertices and 48 edges, with each vertex
Suzuki graph
The Suzuki graph is a strongly regular graph with parameters . Its automorphism group has order 896690995200 and contains as a subgroup of order 2 the Suzuki sporadic group. It is named for Michio Suz
Conference graph
In the mathematical area of graph theory, a conference graph is a strongly regular graph with parameters v, k = (v − 1)/2, λ = (v − 5)/4, and μ = (v − 1)/4. It is the graph associated with a symmetric
Higman–Sims graph
In mathematical graph theory, the Higman–Sims graph is a 22-regular undirected graph with 100 vertices and 1100 edges. It is the unique strongly regular graph srg(100,22,0,6), where no neighboring pai
Conway's 99-graph problem
In graph theory, Conway's 99-graph problem is an unsolved problem asking whether there exists an undirected graph with 99 vertices, in which each two adjacent vertices have exactly one common neighbor
Games graph
In graph theory, the Games graph is the largest known locally linear strongly regular graph. Its parameters as a strongly regular graph are (729,112,1,20). This means that it has 729 vertices, and 408
Cameron graph
The Cameron graph is a strongly regular graph of parameters .
Chang graphs
In the mathematical field of graph theory, the Chang graphs are a set of three 12-regular undirected graphs, each with 28 vertices and 168 edges. They are strongly regular, with the same parameters an
Schläfli graph
In the mathematical field of graph theory, the Schläfli graph, named after Ludwig Schläfli, is a 16-regular undirected graph with 27 vertices and 216 edges. It is a strongly regular graph with paramet
M22 graph
The M22 graph, also called the Mesner graph or Witt graph is the unique strongly regular graph with parameters (77, 16, 0, 4). It is constructed from the Steiner system (3, 6, 22) by representing its
Petersen graph
In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many prob
Strongly regular graph
In graph theory, a strongly regular graph (SRG) is defined as follows. Let G = (V, E) be a regular graph with v vertices and degree k. G is said to be strongly regular if there are also integers λ and
Hoffman–Singleton graph
In the mathematical field of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique strongly regular graph with parameters (50,7,0,1