CageGraph

As of Version 10, most of the functionality of the Combinatorica package is built into the Wolfram System. >>

CageGraph[k,r]
gives a smallest k-regular graph of girth r for certain small values of k and r. For k=3, r can be 3, 4, 5, 6, 7, 8, or 10. For k=4 or 5, r can be 3, 4, 5, or 6.

CageGraph[r]
gives CageGraph[3,r].

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