=Paper=
{{Paper
|id=Vol-3792/invited3
|storemode=property
|title=Generating and Cataloging Symmetric Graphs
 (invited paper)
|pdfUrl=https://ceur-ws.org/Vol-3792/invited3.pdf
|volume=Vol-3792
|authors=Primož Potočnik
|dblpUrl=https://dblp.org/rec/conf/itat/Potocnik24
}}
==Generating and Cataloging Symmetric Graphs
 (invited paper)==
<pdf width="1500px">https://ceur-ws.org/Vol-3792/invited3.pdf</pdf>
<pre>
                                Generating and cataloging symmetric graphs⋆
                                Primož Potočnik∗
                                University of Ljubljana, Slovenia


                                                                             Abstract
                                                                             Symmetry is a concept which plays a significant role in many areas of human activity. In mathematics, the desire to understand
                                                                             symmetry gave birth to modern group theory. Even today, groups are often studied in terms of their representations as
                                                                             symmetry groups of fixed mathematical objects, such as graphs. The study of groups acting on graphs, especially highly
                                                                             symmetric graphs, have resulted in many deep theories and ground-breaking results throughout mathematics. When studying
                                                                             a class of discrete objects, it is of profound importance to be able to construct complete lists of the representatives of this class
                                                                             up to a given size. On one hand, such lists (or censuses, as are often called) help us formulate and test conjectures. On the
                                                                             other hand, the lack of practical means of constructing such censuses indicates the lack of understanding of the theory. Thus,
                                                                             development of theory (and, of course, computational resources) enables constructions of complete censuses of objects, while
                                                                             censuses themselves facilitate and motivate further theoretical achievements. Attempts of constructing census of graphs with
                                                                             high level of symmetry began in early 1930s, when Foster started collecting examples of arc- transitive graphs of valence
                                                                             3. His work, now known as Foster’s census, has been a valuable source of information for graph and group theorists for
                                                                             many decades. Several legendary mathematicians have been involved in constructions of catalogues of graphs of specific
                                                                             symmetry types, such as William Tutte, Harold Coxeter, John Conway etc. In the last few decades, Foster’s original work was
                                                                             successfully upgraded in several directions. The aim of the talk is to present the theory and methods behind constructions of
                                                                             these classical censuses, give a few practical demonstrations using modern computer algebra systems, and present some of
                                                                             the more recent achievements in this area.




                                ITAT’24: Information technologies – Applications and Theory, Septem-
                                ber 20–24, 2024, Drienica, Slovakia
                                ∗
                                     Corresponding author.
                                Envelope-Open primoz.potocnik@fmf.uni-lj.si (P. Potočnik)
                                                                       © 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License
                                                                       Attribution 4.0 International (CC BY 4.0).
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                                                  ISSN 1613-0073
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