1. Symmetries of the Woolly Hat graphsLeah Berman, Sergio Hiroki Koike Quintanar, Elías Mochán, Alejandra Ramos Rivera, Primož Šparl, Steve Wilson, 2024, izvirni znanstveni članek Opis: A graph is edge-transitive if the natural action of its automorphism group on its edge set is transitive. An automorphism of a graph is semiregular if all of the orbits of the subgroup generated by this automorphism have the same length. While the tetravalent edge-transitive graphs admitting a semiregular automorphism with only one orbit are easy to determine, those that admit a semiregular automorphism with two orbits took a considerable effort and were finally classified in 2012. Of the several possible different "types" of potential tetravalent edge-transitive graphs admitting a semiregular automorphism with three orbits, only one "type" has thus far received no attention. In this paper we focus on this class of graphs, which we call the Woolly Hat graphs. We prove that there are in fact no edge-transitive Woolly Hat graphs and classify the vertex-transitive ones.
Ključne besede: edge-transitive, vertex-transitive, tricirculant, Woolly Hat graphs
Objavljeno v RUP: 10.09.2025; Ogledov: 647; Prenosov: 7
 Celotno besedilo (552,80 KB) |
2. On 3-isoregularity of multicirculantsKlavdija Kutnar, Dragan Marušič, Štefko Miklavič, 2025, izvirni znanstveni članek Opis: A graph is said to be k-isoregular if any two vertex subsets of cardinality at most k, that induce subgraphs of the same isomorphism type, have the same number of neighbors. It is shown that no 3-isoregular bicirculant (and more generally, no locally 3-isoregular bicirculant) of order twice an odd number exists. Further, partial results for bicirculants of order twice an even number as well as tricirculants of specific orders, are also obtained. Since 3-isoregular graphs are necessarily strongly regular, a motivation for the above result about bicirculants is that it brings us a step closer to obtaining a direct proof of a classical consequence of the Classification of Finite Simple Groups, that no simply primitive group of degree twice a prime exists for primes greater than 5.
Ključne besede: 3-isoregularity, strongly regular graph, bicirculant, tricirculant
Objavljeno v RUP: 06.08.2025; Ogledov: 451; Prenosov: 6
Celotno besedilo (233,35 KB) |
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