Skip to main content Accessibility help
×
Home

Christoffel–Darboux Type Identities for the Independence Polynomial

Published online by Cambridge University Press:  02 April 2018

FERENC BENCS
Affiliation:
Eötvös Loránd Tudományegyetem, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary Central European University, H-1051 Budapest, Nador utca 9, Hungary (e-mail: bencs.ferenc@renyi.mta.hu)
Corresponding
E-mail address:

Abstract

In this paper we introduce some Christoffel–Darboux type identities for independence polynomials. As an application, we give a new proof of a theorem of Chudnovsky and Seymour, which states that the independence polynomial of a claw-free graph has only real roots. Another application is related to a conjecture of Merrifield and Simmons.

Type
Paper
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below.

References

[1] Chihara, T. S. (2011) An Introduction to Orthogonal Polynomials, Courier Corporation.Google Scholar
[2] Chudnovsky, M. and Seymour, P. (2007) The roots of the independence polynomial of a clawfree graph. J. Combin. Theory Ser. B 97 350357.CrossRefGoogle Scholar
[3] Godsil, C. D. (1993) Algebraic Combinatorics, Vol. 6, CRC Press.Google Scholar
[4] Gutman, I. (1990) Graph propagators. In Graph Theory Notes of New York, Vol. XIX, The New York Academy of Sciences, pp. 2630.Google Scholar
[5] Heilmann, O. J. and Lieb, E. H. (1972) Theory of monomer–dimer systems. Comm. Math. Phys. 25 190232.CrossRefGoogle Scholar
[6] Lass, B. (2012) Mehler formulae for matching polynomials of graphs and independence polynomials of clawfree graphs. J. Combin. Theory Ser. B 102 411423.CrossRefGoogle Scholar
[7] Levit, V. E. and Mandrescu, E. (2005) The independence polynomial of a graph: A survey. In 1st International Conference on Algebraic Informatics (Bozapalidis, S. et al., eds), Aristotle University of Thessaloniki, pp. 233254.Google Scholar
[8] Merrifield, R. and Simmons, H. (1989) Topological Methods in Chemistry, Wiley.Google Scholar
[9] Trinks, M. (2013) The Merrifield–Simmons conjecture holds for bipartite graphs. J. Graph Theory 72 478486.CrossRefGoogle 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: 62 *
View data table for this chart

* Views captured on Cambridge Core between 02nd April 2018 - 24th January 2021. This data will be updated every 24 hours.

Hostname: page-component-76cb886bbf-r88h9 Total loading time: 0.898 Render date: 2021-01-24T23:05:31.616Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false }

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.

Christoffel–Darboux Type Identities for the Independence Polynomial
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.

Christoffel–Darboux Type Identities for the Independence Polynomial
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.

Christoffel–Darboux Type Identities for the Independence Polynomial
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *