On the automorphism groups of almost all circulant graphs and digraphs

Simple item page
dc.contributor.authorBhoumik, Soumya
dc.contributor.authorDobson, Edward
dc.contributor.authorMorris, Joy
dc.date.accessioned2025-12-13T22:07:15Z
dc.date.available2025-12-13T22:07:15Z
dc.date.issued2014
dc.descriptionOpen access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
dc.description.abstractWe attempt to determine the structure of the automorphism group of a generic circulant graph. We first show that almost all circulant graphs have automorphism groups as small as possible. The second author has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism group is not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose order is in a "large" subset of integers. We note that all non-normal circulant (di)graphs can be classified into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraph.
dc.description.peer-reviewYes
dc.identifier.citationBhoumik, S., Dobson, E., & Morris, J. (2014). On the automorphism groups of almost all circulant graphs and digraphs. Ars Mathematica Contemporanea, 7(2), 487-506. https://doi.org/10.26493/1855-3974.315.868
dc.identifier.urihttps://hdl.handle.net/10133/7261
dc.language.isoen
dc.publisherUniversity of Primorska
dc.publisherThe Slovenian Discrete and Applied Mathematics Society
dc.publisher.departmentDepartment of Mathematics and Computer Science
dc.publisher.facultyArts and Science
dc.publisher.institutionFort Hayes State University
dc.publisher.institutionMississippi State University
dc.publisher.institutionUniversity of Lethbridge
dc.publisher.urlhttps://doi.org/10.26493/1855-3974.315.868
dc.subjectCirculant graph
dc.subjectAutomorphism group
dc.subjectCayley graph
dc.subjectDRR
dc.subjectGRR
dc.subjectDigraph
dc.titleOn the automorphism groups of almost all circulant graphs and digraphs
dc.typeArticle
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Morris-on-the-automorphism.pdf
Size:
5.04 MB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
1.75 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Morris, Joy