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On tetravalent half-arc-transitive graphs of girth 5Antončič, Iva, 1986- ; Šparl, PrimožA subgroup of the automorphism group of a graph is said to be half-arc-transitive on ▫$\Gamma$▫ if its action on ▫$\Gamma$▫ is transitive on the vertex set of ▫$\Gamma$▫ and on the edge set of ... ▫$\Gamma$▫ but not on the arc set of ▫$\Gamma$▫. Tetravalent graphs of girths ▫$3$▫ and ▫$4$▫ admitting a half-arc-transitive group of automorphisms have previously been characterized. In this paper we study the examples of girth ▫$5$▫. We show that, with two exceptions, all such graphs only have directed ▫$5$▫-cycles with respect to the corresponding induced orientation of the edges. Moreover, we analyze the examples with directed ▫$5$▫-cycles, study some of their graph theoretic properties and prove that the ▫$5$▫-cycles of such graphs are always consistent cycles for the given half-arc-transitive group. We also provide infinite families of examples, classify the tetravalent graphs of girth ▫$5$▫ admitting a half-arc-transitive group of automorphisms relative to which they are tightly-attached and classify the tetravalent half-arc-transitive weak metacirculants of girth ▫$5$▫.Source: Discrete mathematics. - ISSN 0012-365X (Vol. 346, iss. 10, art. 113577, 2023, str. 1-17)Type of material - article, component part ; adult, seriousPublish date - 2023Language - englishCOBISS.SI-ID - 157544707
Author
Antončič, Iva, 1986- |
Šparl, Primož
Topics
tetravalent graph |
half-arc-transitive |
girth 5 |
consistent cycle |
štirivalenten graf |
poltranzitiven |
ožina 5 |
konsistentni cikli
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Antončič, Iva, 1986- | 34602 |
Šparl, Primož | 23341 |
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