Elementary proofs of the diameter bounds for the power graphs
Marco Barbieri, Kamilla Rekv\'enyi
TL;DR
This paper provides simplified proofs demonstrating that, excluding isolated vertices, the complements of the enhanced power graph and the power graph are connected with a diameter of at most 3.
Contribution
It offers a streamlined proof approach for diameter bounds in power graphs, improving understanding of their connectivity properties.
Findings
Complement of the enhanced power graph is connected with diameter ≤ 3
Complement of the power graph is connected with diameter ≤ 3
Simplified proofs enhance comprehension of power graph properties
Abstract
We give a simplified version of the proofs that, outside of their isolated vertices, the complement of the enhanced power graph and of the power graph are connected of diameter at most .
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research