Standard

Fixed points of cyclic groups acting purely harmonically on a graph. / Mednykh, A. D.

в: Siberian Electronic Mathematical Reports, Том 18, № 1, 43, 2021, стр. 617-621.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Mednykh, AD 2021, 'Fixed points of cyclic groups acting purely harmonically on a graph', Siberian Electronic Mathematical Reports, Том. 18, № 1, 43, стр. 617-621. https://doi.org/10.33048/semi.2021.18.044

APA

Mednykh, A. D. (2021). Fixed points of cyclic groups acting purely harmonically on a graph. Siberian Electronic Mathematical Reports, 18(1), 617-621. [43]. https://doi.org/10.33048/semi.2021.18.044

Vancouver

Mednykh AD. Fixed points of cyclic groups acting purely harmonically on a graph. Siberian Electronic Mathematical Reports. 2021;18(1):617-621. 43. doi: 10.33048/semi.2021.18.044

Author

Mednykh, A. D. / Fixed points of cyclic groups acting purely harmonically on a graph. в: Siberian Electronic Mathematical Reports. 2021 ; Том 18, № 1. стр. 617-621.

BibTeX

@article{3686afe98f714ea890f053930f861279,
title = "Fixed points of cyclic groups acting purely harmonically on a graph",
abstract = "Let X be a finite connected graph, possibly with loops and multiple edges. An automorphism group of X acts purely harmonically if it acts freely on the set of directed edges of X and has no invertible edges. Define a genus g of the graph X to be the rank of the first homology group. A discrete version of the Wiman theorem states that the order of a cyclic group ℤn acting purely harmonically on a graph X of genus g > 1 is bounded from above by 2g + 2. In the present paper, we investigate how many fixed points has an automorphism generating a «large» cyclic group ℤn of order n > 2g — 1. We show that in the most cases, the automorphism acts fixed point free, while for groups of order 2g and 2g — 1 it can have one or two fixed points.",
keywords = "fixed point, graph, harmonic automorphism, homological genus, Wiman theorem",
author = "Mednykh, {A. D.}",
note = "Funding Information: Mednykh, A.D., Fixed points of cyclic groups acting purely harmonically on a graph. {\textcopyright} 2021 Mednykh A.D. The study of the author was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0007). Received April, 6, 2021, published June, 2, 2021. Publisher Copyright: {\textcopyright} 2021 Mednykh A.D. All Rights Reserved.",
year = "2021",
doi = "10.33048/semi.2021.18.044",
language = "English",
volume = "18",
pages = "617--621",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - Fixed points of cyclic groups acting purely harmonically on a graph

AU - Mednykh, A. D.

N1 - Funding Information: Mednykh, A.D., Fixed points of cyclic groups acting purely harmonically on a graph. © 2021 Mednykh A.D. The study of the author was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0007). Received April, 6, 2021, published June, 2, 2021. Publisher Copyright: © 2021 Mednykh A.D. All Rights Reserved.

PY - 2021

Y1 - 2021

N2 - Let X be a finite connected graph, possibly with loops and multiple edges. An automorphism group of X acts purely harmonically if it acts freely on the set of directed edges of X and has no invertible edges. Define a genus g of the graph X to be the rank of the first homology group. A discrete version of the Wiman theorem states that the order of a cyclic group ℤn acting purely harmonically on a graph X of genus g > 1 is bounded from above by 2g + 2. In the present paper, we investigate how many fixed points has an automorphism generating a «large» cyclic group ℤn of order n > 2g — 1. We show that in the most cases, the automorphism acts fixed point free, while for groups of order 2g and 2g — 1 it can have one or two fixed points.

AB - Let X be a finite connected graph, possibly with loops and multiple edges. An automorphism group of X acts purely harmonically if it acts freely on the set of directed edges of X and has no invertible edges. Define a genus g of the graph X to be the rank of the first homology group. A discrete version of the Wiman theorem states that the order of a cyclic group ℤn acting purely harmonically on a graph X of genus g > 1 is bounded from above by 2g + 2. In the present paper, we investigate how many fixed points has an automorphism generating a «large» cyclic group ℤn of order n > 2g — 1. We show that in the most cases, the automorphism acts fixed point free, while for groups of order 2g and 2g — 1 it can have one or two fixed points.

KW - fixed point

KW - graph

KW - harmonic automorphism

KW - homological genus

KW - Wiman theorem

UR - http://www.scopus.com/inward/record.url?scp=85108826330&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=46265235

U2 - 10.33048/semi.2021.18.044

DO - 10.33048/semi.2021.18.044

M3 - Article

AN - SCOPUS:85108826330

VL - 18

SP - 617

EP - 621

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

M1 - 43

ER -

ID: 34733822