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The complement of enhanced power graph of a finite group
[article]

2022
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arXiv
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pre-print

The enhanced power graph 𝒫_E(G) of a finite group G is the simple undirected graph whose vertex set is G and two distinct vertices x, y are adjacent if x, y ∈⟨ z ⟩ for some z ∈ G. In this article, we give an affirmative answer of the question posed by Cameron [6] which states that: Is it true that the complement of the enhanced power graph 𝒫̅_̅E̅(̅G̅)̅ of a non-cyclic group G has only one connected component apart from isolated vertices? We classify all finite groups G such that the graph

arXiv:2207.04641v1
fatcat:crhjdl7cebhv3fphqo7jfv5sym