Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic...
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the 4-vertex path graph and the 5-vertex cycle graph. There is no known characterization of self-complementary graphs. Every Paley graph is self-complementary...
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numbers, any Paley graph is a circulant graph. Every Möbius ladder is a circulant graph, as is every complete graph. A complete bipartite graph is a circulant...
10 KB (1,310 words) - 17:01, 14 August 2024
Berlekamp–van Lint–Seidel graph is an srg(243, 22, 1, 2). The McLaughlin graph is an srg(275, 112, 30, 56). The Paley graph of order q is an srg(q, (q − 1)/2...
20 KB (3,355 words) - 16:56, 17 June 2024
subgraph, while neither the 17-vertex Paley graph nor its complement contains a copy of K4. Weisstein, Eric W. "Wheel Graph". MathWorld. Rosen, Kenneth H. (2011)...
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graph Cameron graph Petersen graph Hall–Janko graph Hoffman–Singleton graph Higman–Sims graph Paley graph of order 13 Shrikhande graph Schläfli graph...
14 KB (1,251 words) - 14:50, 13 March 2024
locally C4 graph, the icosahedron is the unique connected locally C5 graph, and the Paley graph of order 13 is locally C6. Locally cyclic graphs other than...
10 KB (1,122 words) - 08:52, 18 August 2023
sizes of matrices for which Hadamard matrices exist. The Paley graphs and Paley tournaments in graph theory are closely related, although they do not appear...
13 KB (1,015 words) - 15:55, 8 September 2023
parameters differing by one, it is the only graph that is not a Paley graph. It is also an integral graph, meaning that the eigenvalues of its adjacency...
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the binary representations of the natural numbers, or as an infinite Paley graph that has edges connecting pairs of prime numbers congruent to 1 mod 4...
38 KB (5,168 words) - 03:42, 24 August 2024
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving...
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instance, the nine-vertex Paley graph (the graph of the 3-3 duoprism) is the Cartesian product of two triangles. The Hamming graph H ( d , 3 ) {\displaystyle...
24 KB (3,362 words) - 08:57, 2 January 2024
Cyclic group (section Cycle graph)
graph is a cycle graph, and for an infinite cyclic group with its generator the Cayley graph is a doubly infinite path graph. However, Cayley graphs can...
36 KB (4,113 words) - 03:36, 18 July 2024
≡ 0 mod 4 {\displaystyle m\,\equiv \,0\mod 4} for m < 668. Paley biplane Paley graph Paley, R.E.A.C. (1933). "On orthogonal matrices". Journal of Mathematics...
8 KB (1,496 words) - 11:19, 30 July 2024
-2} , so it is a 3-regular Ramanujan graph. The icosahedral graph is a 5-regular Ramanujan graph. A Paley graph of order q {\displaystyle q} is q − 1...
19 KB (2,689 words) - 01:42, 4 January 2024
Ramsey's theorem (category Theorems in graph theory)
among 6.4 × 1022 different 2-colourings of 16-node graphs, and only one (4, 4, 17) graph (the Paley graph of order 17) among 2.46 × 1026 colourings. (It follows...
62 KB (7,919 words) - 16:00, 13 September 2024
These two graphs are the nine-vertex Paley graph (the graph of the 3-3 duoprism) with parameters (9,4,1,2) and the Berlekamp–van Lint–Seidel graph with parameters...
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regular graph. The Brouwer–Haemers graph has several related algebraic constructions. One of the simplest is as a degree-4 generalized Paley graph: it can...
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Circulant matrix (section In graph theory)
full-length cycle. The Möbius ladders are examples of circulant graphs, as are the Paley graphs for fields of prime order. Davis, Philip J (1970). Circulant...
15 KB (2,912 words) - 10:50, 26 August 2024
toroidal graph, a locally linear graph, a strongly regular graph with parameters (9,4,1,2), the 3 × 3 {\displaystyle 3\times 3} rook's graph, and the Paley graph...
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hexagonal faces. The dual graph for this embedding is isomorphic to the Paley graph of order 13. The chromatic number of the F26A graph is 2. The chromatic...
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various individual (finite) graphs. The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number)...
7 KB (85 words) - 19:28, 12 March 2024
exists a Paley graph with p {\displaystyle p} vertices, representing the numbers modulo p {\displaystyle p} , with two numbers adjacent in the graph if and...
9 KB (1,092 words) - 19:09, 22 October 2023
In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently...
18 KB (2,546 words) - 01:51, 14 July 2024
Quadratic residue (section Graph theory)
quadratic residues. Paley graphs are dense undirected graphs, one for each prime p ≡ 1 (mod 4), that form an infinite family of conference graphs, which yield...
54 KB (5,557 words) - 19:40, 15 May 2024
Conference graphs are known to exist for all small values of v allowed by the restrictions, e.g., v = 5, 9, 13, 17, 25, 29, and (the Paley graphs) for all...
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application in combinatorics, two well known examples being the definition of Paley Graphs and the related construction for Hadamard Matrices. In arithmetic combinatorics...
45 KB (6,162 words) - 13:35, 7 August 2024
Conference matrix (category Algebraic graph theory)
then the Paley graphs provide examples of symmetric conference matrices of order n, by taking S to be the Seidel matrix of the Paley graph. The first...
12 KB (1,719 words) - 03:42, 11 September 2024
action on 11 points, related to the Paley biplane. distanceregular.org page on Livingstone Graph Weisstein, Eric W. "Livingstone Graph". MathWorld. v t e...
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Ruzsa–Szemerédi problem (category Extremal graph theory)
mathematics and extremal graph theory, the Ruzsa–Szemerédi problem or (6,3)-problem asks for the maximum number of edges in a graph in which every edge belongs...
17 KB (2,129 words) - 00:10, 30 April 2024