We prove that all 3-connected 4-regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive. Moreover, by including a fourth operation we obtain an alternative to a procedure by Lehel to generate all connected 4-regular planar graphs from the Octahedron Graph. 0 1993 John Wiley & Sons, Inc.
al REF showed that all 3-connected 4-regular planar graphs can also be generated from the octahedron, using only three operations.
Generating all 3-connected 4-regular planar graphs from the Octahedron Graph
Journal of Graph Theory
Journal of Graph Theory
Computer Science Mathematics