Gray coding planar maps

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.