Gray coding planar maps
Sergey Avgustinovich, Sergey Kitaev, Vladimir N. Potapov, Vincent, Vajnovszki

TL;DR
This paper develops Gray codes for enumerating specific classes of cubic planar maps using beta-description trees, enabling efficient listing where successive maps differ minimally.
Contribution
It introduces a novel Gray coding method for three classes of cubic planar maps via beta-description trees, expanding combinatorial enumeration techniques.
Findings
Successfully cyclically Gray code three classes of cubic planar maps.
Utilizes beta-description trees to achieve Gray coding.
Enhances enumeration efficiency for planar maps.
Abstract
The idea of (combinatorial) Gray codes is to list objects in question in such a way that two successive objects differ in some pre-specified small way. In this paper, we utilize beta-description trees to cyclicly Gray code three classes of cubic planar maps, namely, bicubic planar maps, 3-connected cubic planar maps, and cubic non-separable planar maps.
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Taxonomy
TopicsCellular Automata and Applications · semigroups and automata theory · Mathematical Dynamics and Fractals
