Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic...

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...

graph is a Cayley graph of a cyclic group. Every cycle graph is a circulant graph, as is every crown graph with 2 modulo 4 vertices. The Paley graphs...

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...

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...

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)...

graph Cameron graph Petersen graph Hall–Janko graph Hoffman–Singleton graph Higman–Sims graph Paley graph of order 13 Shrikhande graph Schläfli graph...

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...

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...

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...

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...

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...

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...

-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...

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...

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. (This...

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...

≡ 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...

various individual (finite) graphs. The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number)...

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...

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...

full-length cycle. The Möbius ladders are examples of circulant graphs, as are the Paley graphs for fields of prime order. Davis, Philip J., Circulant Matrices...

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...

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...

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...

action on 11 points, related to the Paley biplane. distanceregular.org page on Livingstone Graph Weisstein, Eric W. "Livingstone Graph". MathWorld. v t e...

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...

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...

application in combinatorics, two well known examples being the definition of Paley Graphs and the related construction for Hadamard Matrices. In arithmetic combinatorics...

only such bundle known, although a generalized construction involving Paley graphs produces other rank 2 sheaves (Sasukara et al. 1993). The zero sets of...