Generating r-regular graphs☆

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Abstract

For each nonnegative integer r, we determine a set of graph operations such that all r-regular loopless graphs can be generated from the smallest r-regular loopless graphs by using these operations. We also discuss possible extensions of this result to r-regular graphs of girth at least g, for each fixed g.

Keywords

Graph generation
Regular graph

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Research partially supported by NSF grant DMS-9970329 and AFOSR grant F49620-01-1-0264.

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