TL;DR
This paper introduces Skolem circles, a new concept related to Skolem sequences and graphs, exploring their properties, enumerating small cases, and establishing some bounds.
Contribution
It defines Skolem circles as weak Skolem labellings of cycle graphs and investigates their relationship with Skolem sequences, providing enumeration and bounds.
Findings
Skolem circles are related to Skolem sequences and graphs.
Small Skolem circles are enumerated.
Some general bounds for Skolem circles are established.
Abstract
Skolem sequences and Skolem labeled graphs have been described and examined for several decades. This note explores weak Skolem labelling of cycle graphs, which we call Skolem circles. The relationship between Skolem sequences and Skolem cirlces is explored, and Skolem circles of small sizes are enumerated, with some loose general bounds established.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Advanced Graph Theory Research