Paley graphs are their own graph distance-2 graphs. Special cases include the cycle graph (5-Paley), - generalized quadrangle (9-Paley), and - Paulus graph (25-Paley).

5 days ago · Paley Construction Hadamard matrices can be constructed using finite field GF () when and is odd. Pick a representation relatively prime to . Then by coloring white (where is the floor …

5 days ago · Paley graphs with a square number (including the (2,1)- generalized quadrangle, which is isomorphic to the 9-Paley graph) satisfy both conditions. The following table summarizes some …

5 days ago · If m is of this form, the matrix can be constructed with a Paley construction. If m is divisible by 4 but not of the form (1), the Paley class is undefined. However, Hadamard matrices have been …

The Paley class of a positive integer m=0 (mod 4) is defined as the set of all possible quadruples (k,e,q,n) where m=2^e (q^n+1), (1) q is an odd prime, and k= {0 if q=0; 1 if q^n-3=0 (mod 4); 2 if q^n …

5 days ago · It can be constructed by dividing six points into three pairs in all fifteen different ways, then connecting sets with common pairs (hence its isomorphism with a Kneser graph).

5 days ago · Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.

5 days ago · The -Paulus graph is isomorphic to the 25- Paley graph. The 25-node Paulus graphs are cospectral, as are the 26-node Paulus graphs, so none of these is determined by spectrum.

A circulant graph is a graph of n graph vertices in which the ith graph vertex is adjacent to the (i+j)th and (i-j)th graph vertices for each j in a list l. The circulant graph Ci_n (1,2,...,|_n/2_|) gives the complete …

Mar 11, 2026 · The first few of these correspond to the trivial graph on one node, the path graph P_4, and the cycle graph C_5. Every self-complementary graph is not only connected, but also traceable …