On polyhedral graphs and their complements
Riccardo Walter Maffucci
TL;DR
This paper characterizes all polyhedral graphs whose complements are also polyhedral, revealing that these are precisely the self-complementary polyhedral graphs, thus providing a complete classification in this area.
Contribution
The paper identifies and characterizes all polyhedral graphs with polyhedral complements, showing they are exactly the self-complementary polyhedral graphs, which was previously unknown.
Findings
All such graphs are self-complementary.
Complete classification of polyhedral graphs with polyhedral complements.
Provides structural insight into polyhedral and self-complementary graphs.
Abstract
We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Graph Labeling and Dimension Problems