Connectedness of the dart digraph and the squared-dart digraph
Primo\v{z} Poto\v{c}nik, Steve Wilson
TL;DR
This paper investigates the properties of dart digraphs and squared dart digraphs, proving they are strongly connected when derived from connected graphs with minimum degree at least 3.
Contribution
It establishes conditions under which dart and squared dart digraphs are strongly connected, extending understanding of their structural properties.
Findings
Dart digraphs are strongly connected for connected graphs with minimum valence ≥ 3.
Squared dart digraphs are strongly connected under the same conditions.
Provides new insights into the connectivity properties of these digraph constructions.
Abstract
In this note we revisit the dart graph and the squared dart digraph constructions and prove that they yield strongly connected digraphs when applied to connected graphs of minimum valence at least 3.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems