Description of paley

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paley

PURPOSE

paley(g,n) --- create a Paley graph with n vertices

SYNOPSIS

function paley(g,n)

DESCRIPTION

 paley(g,n) --- create a Paley graph with n vertices
 In this graph, there is an edge from i to j iff i-j is a square in Z_n.
 Hence, if -1 is not a square in Z_n, an error is generated.

CROSS-REFERENCE INFORMATION

This function calls:

• add add --- add edge(s) to the graph
• resize resize(g,n) --- change the number of vertices in g to n
• rmxy rmxy(g) --- erase g's embedding

This function is called by:

SOURCE CODE

0001 function paley(g,n)
0002 % paley(g,n) --- create a Paley graph with n vertices
0003 % In this graph, there is an edge from i to j iff i-j is a square in Z_n.
0004 % Hence, if -1 is not a square in Z_n, an error is generated.
0005 
0006 if (n <= 1) 
0007     error('n must be at least 2');
0008 end
0009 
0010 squares = unique(mod([1:n-1].^2,n));
0011 
0012 % check if -1 is a square
0013 if ~ismember(n-1,squares)
0014     error('-1 is not a square in Z_n');
0015 end
0016 resize(g,0);
0017 resize(g,n);
0018 rmxy(g);
0019 for v = 1:n
0020     nlist = mod(v+squares,n);
0021     idx = find(nlist == 0);
0022     if length(idx)>0
0023         nlist(idx) = n;
0024     end
0025     for w = nlist
0026         add(g,v,w)
0027     end
0028 end

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