How to computed poley graph in magma give two example with M

How to computed poley graph in magma give two example with Magma code.

Solution

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.

Paley graphs allow graph-theoretic tools to be applied to the number theory of quadratic residues, and have interesting properties that make them useful in graph theory more generally.

Let q be a prime power such that q = 1 (mod 4). That is, q should either be an arbitrary power of a Pythagorean prime (a prime congruent to 1 mod 4) or an even power of an odd non-Pythagorean prime. This choice of q implies that in the unique finite field F_q of order q, the element 1 has a square root.

If a pair {a,b} is included in E, it is included under either ordering of its two elements. For, a b = (b a), and 1 is a square, from which it it follows that a b is a square if and only if b a is a square.

By definition G = (V, E) is the Paley graph of order q.