The co-prime order graph associated with a finite group Article Swipe
Xuanlong Ma
,
Zhong-Hua Wang
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2011.13547
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2011.13547
Let $G$ be a finite group. The co-prime order graph of $G$ is the graph whose vertex set is $G$, and two distinct vertices $x,y$ are adjacent if gcd$(o(x),o(y))$ is either $1$ or a prime, where $o(x)$ and $o(y)$ are the orders of $x$ and $y$, respectively. In this paper, we characterize all finite groups whose co-prime order graphs are complete and classify all finite groups whose co-prime order graphs are planar. Also, we compute the vertex-connectivity of the co-prime order graph of a cyclic group, a dihedral group and a generalized quaternion group, which answers a question by Banerjee (2019). Finally, we prove that, for a fixed positive integer $k$, there are finitely many finite groups whose co-prime order graphs have (non)orientable genus $k$. As applications, we classify all finite groups whose co-prime order graphs have (non)orientable genus one and two.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2011.13547
- https://arxiv.org/pdf/2011.13547
- OA Status
- green
- Cited By
- 2
- References
- 18
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3108588300
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https://openalex.org/W3108588300Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2011.13547Digital Object Identifier
- Title
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The co-prime order graph associated with a finite groupWork title
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preprintOpenAlex work type
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enPrimary language
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2020Year of publication
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2020-11-27Full publication date if available
- Authors
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Xuanlong Ma, Zhong-Hua WangList of authors in order
- Landing page
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https://arxiv.org/abs/2011.13547Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2011.13547Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2011.13547Direct OA link when available
- Concepts
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Combinatorics, Mathematics, Dihedral group, Finite group, Prime (order theory), Vertex (graph theory), Discrete mathematics, Cyclic group, Order (exchange), Graph, Group (periodic table), Chemistry, Finance, Organic chemistry, Abelian group, EconomicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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2Total citation count in OpenAlex
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2021: 2Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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