Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Hostname: page-component-684bc48f8b-vgwqb Total loading time: 0.263 Render date: 2021-04-10T22:08:23.429Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Bulletin of the Australian Mathematical Society Bulletin of the Australian Mathematical Society

Article contents

CHARACTER GRAPHS WITH NONBIPARTITE HAMILTONIAN COMPLEMENT

Part of: Graph theory Representation theory of groups

Published online by Cambridge University Press:  25 November 2019

MAHDI EBRAHIMI [Opens in a new window]
MAHDI EBRAHIMI
Affiliation:
School of Mathematics,Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran email m.ebrahimi.math@ipm.ir
Corresponding
E-mail address:
m.ebrahimi.math@ipm.ir
Get access
Rights & Permissions[Opens in a new window]

Abstract

For a finite group $G$ , let $\unicode[STIX]{x1D6E5}(G)$ denote the character graph built on the set of degrees of the irreducible complex characters of $G$ . In this paper, we obtain a necessary and sufficient condition which guarantees that the complement of the character graph $\unicode[STIX]{x1D6E5}(G)$ of a finite group $G$ is a nonbipartite Hamiltonian graph.

Keywords

character graph character degree Hamiltonian graph

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 05C45: Eulerian and Hamiltonian graphs 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 91 - 95
Check for updates
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

Access options

Get access to the full version of this content by using one of the access options below.
If you should have access and can't see this content please contact technical support.

Footnotes

This research was supported in part by a grant from the School of Mathematics, Institute for Research in Fundamental Sciences (IPM).

References

Akhlaghi, Z., Casolo, C., Dolfi, S., Pacifici, E. and Sanus, L., ‘On the character degree graph of finite groups’, Ann. Mat. Pura Appl., to appear, 20 pages.Google Scholar
Ebrahimi, M., Iranmanesh, A. and Hosseinzadeh, M. A., ‘Hamiltonian character graphs’, J. Algebra 428 (2015), 54–66.CrossRefGoogle Scholar
Huppert, B., Endliche Gruppen I, Die Grundlehren der mathematischen Wissenschaften, 134 (Springer, Berlin–New York, 1967).10.1007/978-3-642-64981-3CrossRefGoogle Scholar
Huppert, B., ‘Some simple groups which are determined by the set of their character degrees I’, Illinois J. Math. 44 (2000), 828–842.CrossRefGoogle Scholar
Isaacs, I. M., Character Theory of Finite Groups (Academic Press, San Diego, CA, 1976).Google Scholar
Lewis, M. L., ‘An overview of graphs associated with character degrees and conjugacy class sizes in finite groups’, Rocky Mountain J. Math. 38(1) (2008), 175–211.CrossRefGoogle Scholar
Lewis, M. L. and White, D. L., ‘Connectedness of degree graphs of non-solvable groups’, J. Algebra 266(1) (2003), 51–76.10.1016/S0021-8693(03)00346-6CrossRefGoogle Scholar
Lewis, M. L. and White, D. L., ‘Non-solvable groups with no prime dividing three character degrees’, J. Algebra 336 (2011), 158–183.CrossRefGoogle Scholar
Manz, O., Staszewski, R. and Willems, W., ‘On the number of components of a graph related to character degrees’, Proc. Amer. Math. Soc. 103(1) (1988), 31–37.CrossRefGoogle Scholar
Sayanjali, Z., Akhlaghi, Z. and Khosravi, B., ‘On the regularity of character degree graphs’, Bull. Aust. Math. Soc. 100(3) (2019), 428–433.10.1017/S0004972719000315CrossRefGoogle Scholar
Tong-Viet, H. P., ‘Groups whose prime graphs have no triangles’, J. Algebra 378 (2013), 196–206.CrossRefGoogle Scholar
White, D. L., ‘Degree graphs of simple linear and unitary groups’, Comm. Algebra 34(8) (2006), 2907–2921.10.1080/00927870600639419CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 46 *
View data table for this chart

* Views captured on Cambridge Core between 25th November 2019 - 10th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

CHARACTER GRAPHS WITH NONBIPARTITE HAMILTONIAN COMPLEMENT
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

CHARACTER GRAPHS WITH NONBIPARTITE HAMILTONIAN COMPLEMENT
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

CHARACTER GRAPHS WITH NONBIPARTITE HAMILTONIAN COMPLEMENT
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *