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arXiv · 2409.02457

On Oriented Diameter of Power Graphs

Deepu Benson·Bireswar Das·Dipan Dey·Jinia Ghosh
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Abstract

In this paper, we study the oriented diameter of power graphs of groups. We show that a $2$-edge connected power graph of a finite group has oriented diameter at most $4$. We prove that the power graph of the cyclic group of order $n$ has oriented diameter $2$ for all $n\neq 1,2,4,6$. For non-cyclic finite nilpotent groups, we show that the oriented diameter of corresponding power graphs is at least $3$. Moreover, we provide necessary and sufficient conditions for the oriented diameter of $2$-edge connected power graphs of finite non-cyclic nilpotent groups to be either $3$ or $4$. This, in turn, gives an algorithm for computing the oriented diameter of the power graph of a given nilpotent group that runs in time polynomial in the size of the group.

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Deepu Benson, Bireswar Das, Dipan Dey, Jinia Ghosh. 2024-09-04. On Oriented Diameter of Power Graphs. https://arxiv.org/abs/2409.02457

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