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Forbidden subgraphs in enhanced power graphs of finite groups

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups whose enhanced power graphs are split and threshold. We also classify all finite nilpotent groups whose enhanced power graphs are chordal graphs and cographs. Finally, we give some families of non-nilpotent groups whose enhanced power graphs are chordal graphs and cographs. These results partly answer a question posed by Peter J. Cameron.

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Authors and Affiliations

  1. School of Science, Xi’an Shiyou University, Xi’an, 710065, China

    Xuanlong Ma & Yanhong She

  2. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, 21000, Serbia

    Samir Zahirović

  3. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, China

    Yubo Lv

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  1. Xuanlong Ma
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Correspondence to Samir Zahirović.

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Xuanlong Ma’s research is supported by National Natural Science Foundation of China (Grant No. 12326333) and Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSQ024). Samir Zahirović acknowledges financial support of the Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. 451-03-68/2022-14/200125). Yanhong She’s research is supported by National Natural Science Foundation of China (Grant No. 61976244).

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Ma, X., Zahirović, S., Lv, Y. et al. Forbidden subgraphs in enhanced power graphs of finite groups. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 110 (2024). https://doi.org/10.1007/s13398-024-01611-1

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