algebraic graph theory dissertation

Algebraic Graph Theory

• © 2001
• Chris Godsil 0 ,
• Gordon Royle 1

Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada

You can also search for this author in PubMed   Google Scholar

Department of Computer Science, University of Western Australia, Nedlands, Australia

• Includes supplementary material: sn.pub/extras

Part of the book series: Graduate Texts in Mathematics (GTM, volume 207)

200k Accesses

3489 Citations

9 Altmetric

This is a preview of subscription content, log in via an institution to check access.

Access this book

• Available as EPUB and PDF
• Read on any device
• Instant download
• Own it forever
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info
• Durable hardcover edition

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (17 chapters)

Front matter.

• Chris Godsil, Gordon Royle

Transitive Graphs

Arc-transitive graphs, generalized polygons and moore graphs, homomorphisms, kneser graphs.

• Matrix Theory

Interlacing

Strongly regular graphs, line graphs and eigenvalues, the laplacian of a graph, cuts and flows, the rank polynomial, knots and eulerian cycles, back matter.

• graph theory
• homomorphism
• Laplace operator
• combinatorics

Authors and Affiliations

Chris Godsil

Gordon Royle

Bibliographic Information

Book Title : Algebraic Graph Theory

Authors : Chris Godsil, Gordon Royle

Series Title : Graduate Texts in Mathematics

DOI : https://doi.org/10.1007/978-1-4613-0163-9

Publisher : Springer New York, NY

eBook Packages : Springer Book Archive

Copyright Information : Springer-Verlag New York, Inc. 2001

Hardcover ISBN : 978-0-387-95241-3 Published: 20 April 2001

Softcover ISBN : 978-0-387-95220-8 Published: 20 April 2001

eBook ISBN : 978-1-4613-0163-9 Published: 01 December 2013

Series ISSN : 0072-5285

Series E-ISSN : 2197-5612

Edition Number : 1

Number of Pages : XIX, 443

Topics : Combinatorics

• Publish with us

Policies and ethics

• Find a journal
• Track your research

• My Account |
• StudentHome |
• TutorHome |
• IntranetHome |
• Contact the OU Contact the OU Contact the OU |
• Accessibility Accessibility

Postgraduate

• International
• News & media
• Business & apprenticeships
• Contact Contact Contact
• A to Z of courses
• Course types
• Masters degrees
• Postgraduate diplomas
• Postgraduate certificates
• Microcredentials
• Postgraduate modules
• Postgraduate distance learning
• Postgraduate qualifications
• Postgraduate entry requirements
• How will I study?
• Tutors and assessment
• Support, networking and community
• Disability support
• Fees and funding
• Postgraduate loan
• Credit or debit card
• Employer sponsorship
• Mixed payments
• Credit transfer
• OU bursaries
• Grant funding
• Study costs funding
• Carers' Bursary
• Care Experienced Bursary
• Disability financial assistance
• STEMM bursary
• Over 60s bursary
• Creative Writing Scholarship
• Hayes Postgraduate Scholarship
• Disabled Veterans' Scholarships
• How to apply
• Research degrees
• Research areas
• Degrees we offer
• Fees and studentships
• Application process
• Being an OU research student
• Student views

Dissertation in mathematics

This module enables you to carry out a sustained, guided, independent study of a topic in mathematics. There’s a choice of topics, for example: algebraic graph theory; aperiodic tilings and symbolic dynamics; advances in approximation theory; history of modern geometry; interfacial flows and microfluidics; variational methods, and Riemann surfaces. Provided study notes, books, research articles, and original sources guide you. You must master the appropriate mathematics and present your work as a final dissertation.

Qualifications

M840 is a compulsory module in our:

• MSc in Mathematics (F04)
• Credits measure the student workload required for the successful completion of a module or qualification.
• One credit represents about 10 hours of study over the duration of the course.
• You are awarded credits after you have successfully completed a module.
• For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.

Find out more about entry requirements .

What you will study

The list of topics available varies each year. We’ll let MSc in Mathematics students know the available topics that October in the spring, before the module starts.

Recently available topics have included:

• Advances in approximation theory
• Algebraic graph theory
• Aperiodic tilings and symbolic dynamics
• History of modern geometry
• Interfacial flows and microfluidics
• Riemann surfaces
• Variational methods.

Please note:

• Since the available topics vary from year to year, check that we are offering the topic you wish to study before registering.
• For staffing reasons, you might not be able to study your preferred topic. Therefore, we’ll ask you for your first and second choice. We can usually offer you one of your choices, although this cannot be guaranteed.

You will learn

Successful study of this module should enhance your skills in understanding complex mathematical texts, working on open-ended problems and communicating mathematical ideas clearly.

Teaching and assessment

Support from your tutor.

Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:

• Marking your assignments (TMAs) and providing detailed feedback for you to improve.
• Guiding you to additional learning resources.
• Providing individual guidance, whether that’s for general study skills or specific module content.

The module has a dedicated and moderated forum where you can join in online discussions with your fellow students. There are also online module-wide tutorials. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part. If you want to participate, you’ll likely need a headset with a microphone.

The assessment details can be found in the facts box.

Course work includes

Future availability.

Dissertation in mathematics (M840) starts once a year – in October.

This page describes the module that will start in October 2024.

We expect it to start for the last time in October 2029.

Regulations

Entry requirements.

You must have passed four modules from the MSc in Mathematics (F04) .

If you’ve passed only three modules, you may request exceptional permission to take M840 alongside another module.

Additionally:

• To study the ‘Advances in approximation theory’ topic, you should have passed Advanced mathematical methods (M833) or the discontinued module M832.
• To study the ‘Variational methods applied to eigenvalue problems’ topic, you should have passed Calculus of variations and advanced calculus (M820) .
• To study the ‘Riemann surfaces’ topic, you should have a Grade 1 or 2 pass a course in Complex analysis (M337) or an equivalent course.

All teaching is in English and your proficiency in the English language should be adequate for the level of study you wish to take. We strongly recommend that students have achieved an IELTS (International English Language Testing System) score of at least 7. To assess your English language skills in relation to your proposed studies you can visit the IELTS website.

Additional costs

Study costs.

There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.

Study events

This module may have an optional in-person study event. We’ll let you know if this event will take place and any associated costs as soon as we can.

Ways to pay for this module

We know there’s a lot to think about when choosing to study, not least how much it’s going to cost and how you can pay.

That’s why we keep our fees as low as possible and offer a range of flexible payment and funding options, including a postgraduate loan, if you study this module as part of an eligible qualification. To find out more, see Fees and funding .

Study materials

What's included.

You’ll have access to a module website, which includes:

• a week-by-week study planner
• course-specific module materials
• audio and video content
• assessment details and submission section
• online tutorial access.

You will need

Some topics require specific books. We’ll let you know which once your topic is confirmed.

Computing requirements

You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Ventura or higher.

Any additional software will be provided or is generally freely available.

To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).

Our module websites comply with web standards, and any modern browser is suitable for most activities.

Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.

It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop, as described above.

If you have a disability

The material contains small print and diagrams, which may cause problems if you find reading text difficult. Adobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components may not be available or fully accessible using a screen reader and mathematical materials may be particularly difficult to read in this way. Alternative formats of the study materials may be available in the future.

To find out more about what kind of support and adjustments might be available, contact us or visit our disability support pages .

Request your prospectus

Our prospectuses help you choose your course, understand what it's like to be an OU student and register for study.

Request prospectus    

The Open University

• Study with us
• Supported distance learning
• Funding your studies
• International students
• Global reputation
• Apprenticeships
• Develop your workforce
• Contact the OU

Undergraduate

• Arts and Humanities
• Art History
• Business and Management
• Combined Studies
• Computing and IT
• Counselling
• Creative Writing
• Criminology
• Early Years
• Electronic Engineering
• Engineering
• Environment
• Film and Media
• Health and Social Care
• Health and Wellbeing
• Health Sciences
• International Studies
• Mathematics
• Mental Health
• Nursing and Healthcare
• Religious Studies
• Social Sciences
• Social Work
• Software Engineering
• Sport and Fitness
• Postgraduate study
• Masters in Art History (MA)
• Masters in Computing (MSc)
• Masters in Creative Writing (MA)
• Masters degree in Education
• Masters in Engineering (MSc)
• Masters in English Literature (MA)
• Masters in History (MA)
• Master of Laws (LLM)
• Masters in Mathematics (MSc)
• Masters in Psychology (MSc)
• A to Z of Masters degrees
• Accessibility statement
• Conditions of use
• Privacy policy
• Cookie policy
• Manage cookie preferences
• Modern slavery act (pdf 149kb)

Follow us on Social media

• Student Policies and Regulations
• Student Charter
• System Status
• Contact the OU Contact the OU
• Modern Slavery Act (pdf 149kb)

© . . .

• Bibliography
• More Referencing guides Blog Automated transliteration Relevant bibliographies by topics
• Automated transliteration
• Relevant bibliographies by topics
• Referencing guides

Dissertations / Theses on the topic 'Graph theory'

Create a spot-on reference in apa, mla, chicago, harvard, and other styles.

Consult the top 50 dissertations / theses for your research on the topic 'Graph theory.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.

Bessy, Stéphane. "Some problems in graph theory and graphs algorithmic theory." Habilitation à diriger des recherches, Université Montpellier II - Sciences et Techniques du Languedoc, 2012. http://tel.archives-ouvertes.fr/tel-00806716.

Myers, Joseph Samuel. "Extremal theory of graph minors and directed graphs." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619614.

Johnson, Chase R. "Molecular Graph Theory." Digital WPI, 2010. https://digitalcommons.wpi.edu/etd-theses/1179.

Feghali, Carl. "Topics in graph colouring and extremal graph theory." Thesis, Durham University, 2016. http://etheses.dur.ac.uk/11790/.

Nikwigize, Adolphe. "Graph theory : Route problems." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-17397.

Berg, Deborah. "Connections Between Voting Theory and Graph Theory." Scholarship @ Claremont, 2005. https://scholarship.claremont.edu/hmc_theses/178.

Hatt, Justin Dale. "Online assessment of graph theory." Thesis, Brunel University, 2016. http://bura.brunel.ac.uk/handle/2438/13389.

Keevash, Peter. "Topics in extremal graph theory." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619938.

Law, Ka-ho, and 羅家豪. "Some results in graph theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44899816.

Morrison, Julie Lindsay. "Computational graph theory in bioinformatics." Thesis, University of Strathclyde, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435114.

Richer, Duncan Christopher. "Graph theory and combinatorial games." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621916.

Eggemann, Nicole. "Some applications of graph theory." Thesis, Brunel University, 2009. http://bura.brunel.ac.uk/handle/2438/3953.

Nieh, Ari. "Fractional Analogues in Graph Theory." Scholarship @ Claremont, 2001. https://scholarship.claremont.edu/hmc_theses/131.

Reed, Bruce. "A semi-strong perfect graph theorem /." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=72812.

Letzter, Shoham. "Extremal graph theory with emphasis on Ramsey theory." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709415.

Meek, Darrin Leigh. "On graph approximation heuristics : an application to vertex cover on planar graphs." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/24088.

Zuffi, Lorenzo. "Simplicial Complexes From Graphs Toward Graph Persistence." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13519/.

Anderson, Jon K. "Genetic algorithms applied to graph theory." Virtual Press, 1999. http://liblink.bsu.edu/uhtbin/catkey/1136714.

Peng, Richard. "Algorithm Design Using Spectral Graph Theory." Research Showcase @ CMU, 2013. http://repository.cmu.edu/dissertations/277.

Islam, Mustafa R. "A hypertext graph theory reference system." Virtual Press, 1993. http://liblink.bsu.edu/uhtbin/catkey/879844.

Edwards, C. S. "Some extremal problems in graph theory." Thesis, University of Reading, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373467.

Garbe, Frederik. "Extremal graph theory via structural analysis." Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8869/.

Grinshpun, Andrey Vadim. "Some problems in Graph Ramsey Theory." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/97767.

Pappone, Francesco. "Graph neural networks: theory and applications." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23893/.

Parks, David J. "Graph theory in America, 1876-1950." Thesis, Open University, 2012. http://oro.open.ac.uk/54663/.

Schuerger, Houston S. "Contributions to Geometry and Graph Theory." Thesis, University of North Texas, 2020. https://digital.library.unt.edu/ark:/67531/metadc1707341/.

Weaver, Robert Wooddell. "Some problems in structural graph theory /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487268021746449.

Florkowski, Stanley F. "Spectral graph theory of the Hypercube." Thesis, Monterey, Calif. : Naval Postgraduate School, 2008. http://edocs.nps.edu/npspubs/scholarly/theses/2008/Dec/08Dec%5FFlorkowski.pdf.

Han, Lin. "Graph generative models from information theory." Thesis, University of York, 2012. http://etheses.whiterose.ac.uk/3726/.

Robinson, Laura Ann. "Graph Theory for the Middle School." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2226.

Loveland, Susan M. "The Reconstruction Conjecture in Graph Theory." DigitalCommons@USU, 1985. https://digitalcommons.usu.edu/etd/7022.

Yi, Peipei. "Graph query autocompletion." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/557.

Hegde, Rajneesh. "New Tools and Results in Graph Structure Theory." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/10481.

Lopez, Christian P. "On the relationship between a graph and the cycle graph of its complement." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 1995. https://ro.ecu.edu.au/theses/1184.

Morisi, Rita. "Graph–based techniques and spectral graph theory in control and machine learning." Thesis, IMT Alti Studi Lucca, 2016. http://e-theses.imtlucca.it/188/1/Morisi_phdthesis.pdf.

Hoang, Chinh T. "Perfect graphs." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74011.

Hayward, Ryan B. "Two classes of perfect graphs." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74025.

Olariu, Stephan. "Results on perfect graphs." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=73997.

Waterhouse, Mary Alexandra Paula Royston Hastilow. "Coloured graph decompositions /." [St. Lucia, Qld.], 2005. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18769.pdf.

Weinstein, Lee. "Empirical study of graph properties with particular interest towards random graphs." Diss., Connect to the thesis, 2005. http://hdl.handle.net/10066/1485.

Narayanan, Bhargav. "Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/252850.

Fiala, Nick C. "Some topics in combinatorial design theory and algebraic graph theory /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486402957198077.

Burns, Jonathan. "Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5193.

Turner, Bethany. "Embeddings of Product Graphs Where One Factor is a Hypercube." VCU Scholars Compass, 2011. http://scholarscompass.vcu.edu/etd/2455.

Srikanthan, T. "Bond graph analysis." Thesis, Coventry University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373896.

Chen, Xujin, and 陳旭瑾. "Graph partitions and integer flows." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30286256.

Vella, Antoine. "A Fundamentally Topological Perspective on Graph Theory." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1033.

Douma, Femke. "Counting and averaging problems in graph theory." Thesis, Durham University, 2010. http://etheses.dur.ac.uk/272/.

Al-Shimary, Abbas. "Applications of graph theory to quantum computation." Thesis, University of Leeds, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608359.

Yilma, Zelealem Belaineh. "Results in Extremal Graph and Hypergraph Theory." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/49.