Simple Groups Whose Gruenberg–Kegel Graph or Solvable Graph is Split

Mark L. Lewis; J. Mirzajani; A. R. Moghaddamfar; A. V. Vasil’ev; M. A. Zvezdina

doi:10.1007/s40840-019-00815-8

Simple Groups Whose Gruenberg–Kegel Graph or Solvable Graph is Split

Mark L. Lewis, J. Mirzajani, A. R. Moghaddamfar, A. V. Vasil’ev, M. A. Zvezdina

Section of Algebra and Mathematical Logic

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

A graph is split if there is a partition of its vertex set into a clique and an independent set. In this paper, we determine when the Gruenberg–Kegel graph, the solvable graph, and the compact forms of these graphs associated with finite nonabelian simple groups are split. In particular, it is proved that the compact form of the Gruenberg–Kegel graph of any finite simple group is split.

Original language	English
Pages (from-to)	2523-2547
Number of pages	25
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	43
Issue number	3
DOIs	https://doi.org/10.1007/s40840-019-00815-8
Publication status	Published - 1 May 2020

Keywords

Gruenberg–Kegel graph
Simple group
Solvable graph
Split graph
RECOGNITION
ORDERS
FINITE-GROUPS
COMPONENTS
PRIME GRAPH
Gruenberg-Kegel graph

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abstract = "A graph is split if there is a partition of its vertex set into a clique and an independent set. In this paper, we determine when the Gruenberg–Kegel graph, the solvable graph, and the compact forms of these graphs associated with finite nonabelian simple groups are split. In particular, it is proved that the compact form of the Gruenberg–Kegel graph of any finite simple group is split.",

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AU - Mirzajani, J.

AU - Moghaddamfar, A. R.

AU - Vasil’ev, A. V.

AU - Zvezdina, M. A.

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AB - A graph is split if there is a partition of its vertex set into a clique and an independent set. In this paper, we determine when the Gruenberg–Kegel graph, the solvable graph, and the compact forms of these graphs associated with finite nonabelian simple groups are split. In particular, it is proved that the compact form of the Gruenberg–Kegel graph of any finite simple group is split.

KW - Gruenberg–Kegel graph

KW - Simple group

KW - Solvable graph

KW - Split graph

KW - RECOGNITION

KW - ORDERS

KW - FINITE-GROUPS

KW - COMPONENTS

KW - PRIME GRAPH

KW - Gruenberg-Kegel graph

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JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

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ER -

Simple Groups Whose Gruenberg–Kegel Graph or Solvable Graph is Split

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Keywords

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