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arXiv · 1807.00289

Generalized power graph of groups

Abbas Jafarzadeh·Peyman Niroomand·Mohsen Parvizi
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Abstract

The power graph of an arbitrary group $G$ is a simple graph with all elements of $G$ as its vertices and two vertices are adjacent if one is a positive power of another. In this paper, we generalize this concept to a graph whose vertices are all elements of $G$ that generate a proper subgroup of $G$ and two elements are adjacent if the cyclic subgroup generated by which have non-trivial intersections. We concentrate on completeness and planarity of this graph.

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Abbas Jafarzadeh, Peyman Niroomand, Mohsen Parvizi. 2018-07-01. Generalized power graph of groups. https://arxiv.org/abs/1807.00289

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