Geodesic
Recursive generation of simple planar quadrangulations with vertices of degree 3 and 4
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 123-136

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We describe how the simple planar quadrangulations with vertices of degree 3 and 4, whose duals are known as octahedrites, can all be obtained from an elementary family of starting graphs by repeatedly applying two expansion operations. This allows for construction of a linear time generator of all graphs in the class with at most a given order, up to isomorphism.
Keywords: planar graph, octahedrite, quadrangulation, generation 
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Hasheminezhad, Mahdieh; McKay, Brendan. Recursive generation of simple planar quadrangulations with vertices of degree 3 and 4. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 123-136. http://geodesic.mathdoc.fr/item/DMGT_2010_30_1_a10/