Finite groups with star-free noncyclic graphs-Reference-Cited by-同舟云学术

Finite groups with star-free noncyclic graphs

Published:2019-08-08 Issue:1 Volume:17 Page:906-912
ISSN:2391-5455
Container-title:Open Mathematics
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Author:

Ma Xuanlong¹,Walls Gary L.²,Wang Kaishun³

Affiliation:

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

2. Department of Mathematics, Southeastern Louisiana University, Hammond, LA 70402, USA

3. Math. Sci. & Lab. Math. Com. Sys., Beijing Normal University, Beijing, 100875, P.R. China

Abstract

Abstract For a finite noncyclic group G, let Cyc(G) be the set of elements a of G such that 〈a, b〉 is cyclic for each b of G. The noncyclic graph of G is a graph with the vertex set G ∖ Cyc(G), having an edge between two distinct vertices x and y if 〈x, y〉 is not cyclic. In this paper, we classify all finite noncyclic groups whose noncyclic graphs are K1,n-free, where K1,n is a star and 3 ≤ n ≤ 6.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2019-0071/pdf

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