On neighborhoods in the enhanced power graph associated with a finite group

Published 29 Aug 2024 in math.GR | (2408.16545v1)

Abstract: This article investigates neighborhoods' sizes in the enhanced power graph (as known as the cyclic graph) associated with a finite group. In particular, we characterize finite $p$-groups with the smallest maximum size for neighborhoods of nontrivial element in its enhanced power graph.

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