DMGT

Discussiones Mathematicae Graph Theory 30(1) (2010) 123-136
DOI: https://doi.org/10.7151/dmgt.1482

RECURSIVE GENERATION OF SIMPLE PLANAR QUADRANGULATIONS WITH VERTICES OF DEGREE 3 AND 4

Mahdieh Hasheminezhad

Department of Computer Science
Faculty of Mathematics and Computer Science
Amirkabir University of Technology, Tehran, Iran
e-mail: [email protected]

Brendan D. McKay

School of Computer Science
Australian National University
ACT 0200, Australia
e-mail: [email protected]

Abstract

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.

2010 Mathematics Subject Classification: 05C10, 05C85.

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Received 25 June 2008
Revised 28 April 2009
Accepted 28 April 2009