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Title: Cubic factor-invariant graphs of cycle quotient type—the alternating case Authors: ID Alspach, Brian (Author) ID Šparl, Primož (Author) Files: PDF - Presentation file, download (603,84 KB) MD5: 504AFBFCDCFC737ED83D67F398891F8E   URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0195669824000490?via%3Dihub   Language: English Typology: 1.01 - Original Scientific Article Organization: IMFM - Institute of Mathematics, Physics, and Mechanics Abstract: We investigate connected cubic vertex-transitive graphs whose edge sets admit a partition into a $2$-factor ${\mathcal C}$ and a $1$-factor that is invariant under a vertex-transitive subgroup of the automorphism group of the graph and where the quotient graph with respect to ${\mathcal C}$ is a cycle. There are two essentially different types of such cubic graphs. In this paper we focus on the examples of what we call the alternating type. We classify all such examples admitting a vertex-transitive subgroup of the automorphism group of the graph preserving the corresponding $2$-factor and also determine the ones for which the $2$-factor is invariant under the full automorphism group of the graph. In this way we introduce a new infinite family of cubic vertex-transitive graphs that is a natural generalization of the well-known generalized Petersen graphs as well as of the honeycomb toroidal graphs. The family contains an infinite subfamily of arc-regular examples and an infinite subfamily of $2$-arc-regular examples. Keywords: cubic vertex-transitive graphs Publication status: Published Publication version: Version of Record Publication date: 01.01.2024 Year of publishing: 2024 Number of pages: 22 str. Numbering: Vol. 120, art. no. 103964 PID: 20.500.12556/DiRROS-20456  UDC: 519.17 ISSN on article: 1095-9971 DOI: 10.1016/j.ejc.2024.103964  COBISS.SI-ID: 194455299  Publication date in DiRROS: 19.09.2024 Views: 206 Downloads: 111 Metadata:    Cite this work Plain text BibTeX EndNote XML EndNote/Refer RIS ABNT ACM Ref AMA APA Chicago 17th Author-Date Harvard IEEE ISO 690 MLA Vancouver : Copy citation

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Record is a part of a journal

Title:	European journal of combinatorics
Shortened title:	Eur. j. comb.
Publisher:	Elsevier
ISSN:	1095-9971
COBISS.SI-ID:	53351683

Document is financed by a project

Funder:	ARIS - Slovenian Research and Innovation Agency
Project number:	P1-0285
Name:	Algebra, diskretna matematika, verjetnostni račun in teorija iger

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Funder:	ARIS - Slovenian Research and Innovation Agency
Project number:	J1-3001
Name:	Terwilligerjeva algebra grafa

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Funder:	ARIS - Slovenian Research and Innovation Agency
Project number:	J1-50000
Name:	Hamiltonski cikli z rotacijsko simetrijo v povezanih točkovno tranzitivnih grafih

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License:	CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:	http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:	The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

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