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arXiv · 2511.11926

The commuting graph and a graph associated with centralizers

Mark L. Lewis·Ryan McCulloch
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Abstract

Let $G$ be a $p$-group. We begin to consider the relationship between the structure of the commuting graph and $|G:Z(G)|$. We also build a family of groups whose commuting graphs have more than one connected component whose diameter is at least $2$. For this, we introduce another graph related to the commuting graph that is associated with centralizers.

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Mark L. Lewis, Ryan McCulloch. 2025-11-14. The commuting graph and a graph associated with centralizers. https://arxiv.org/abs/2511.11926

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