# generateRandomRegularGraphs -- generates random regular graphs on a given number of vertices

## Synopsis

• Usage:
G = generateRandomRegularGraphs(n, num, reg)
G = generateRandomRegularGraphs(R, num, reg)
• Inputs:
• R, , the ring in which the graphs will be created
• n, an integer, the number of vertices of the graphs
• num, an integer, the number of random graphs to generate
• reg, an integer, the regularity of the generated graphs
• Optional inputs:
• RandomSeed => an integer, default value 0, if nonzero, then the specified random seed is passed to nauty
• Outputs:
• G, a list, the randomly generated regular graphs

## Description

This method generates a specified number of random graphs on a given number of vertices with a given regularity. Note that some graphs may be isomorphic.

If a PolynomialRing R is supplied instead, then the number of vertices is the number of generators. Moreover, the Strings are automatically converted to graphs in R.

 `i1 : R = QQ[a..e];` ```i2 : generateRandomRegularGraphs(R, 3, 2) o2 = {Graph{edges => {{b, c}, {a, d}, {b, d}, {a, e}, {c, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {a, c}, {b, d}, {c, e}, {d, e}}}, ring => R vertices => {a, b, c, d, e} ------------------------------------------------------------------------ Graph{edges => {{a, b}, {a, c}, {b, d}, {c, e}, {d, e}}}} ring => R vertices => {a, b, c, d, e} o2 : List```