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arXiv · 1901.08187

The degree of a vertex in the power graph of a finite abelian group

Amit Sehgal·Shubh N. Singh
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Abstract

The power graph of a given finite group is a simple undirected graph whose vertex set is the group itself, and there is an edge between any two distinct vertices if one is a power of the other. In this paper, we find a precise formula to count the degree of a vertex in the power graph of a finite abelian group of prime-power order. By using the degree formula, we give a new proof to show that the power graph of a cyclic group of prime-power order is complete. We finally determine the degree of a vertex in the power graph of a finite abelian group.

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Amit Sehgal, Shubh N. Singh. 2019-01-24. The degree of a vertex in the power graph of a finite abelian group. https://arxiv.org/abs/1901.08187

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