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On automorphisms of graphs and Riemann surfaces acting with fixed points. / Gromadzki, G.; Mednykh, A. D.; Mednykh, I. A.

In: Analysis and Mathematical Physics, Vol. 9, No. 4, 01.12.2019, p. 2021-2031.

Research output: Contribution to journal › Article › peer-review

Harvard

Gromadzki, G, Mednykh, AD & Mednykh, IA 2019, 'On automorphisms of graphs and Riemann surfaces acting with fixed points', Analysis and Mathematical Physics, vol. 9, no. 4, pp. 2021-2031. https://doi.org/10.1007/s13324-019-00298-7

APA

Gromadzki, G., Mednykh, A. D., & Mednykh, I. A. (2019). On automorphisms of graphs and Riemann surfaces acting with fixed points. Analysis and Mathematical Physics, 9(4), 2021-2031. https://doi.org/10.1007/s13324-019-00298-7

Vancouver

Gromadzki G, Mednykh AD, Mednykh IA. On automorphisms of graphs and Riemann surfaces acting with fixed points. Analysis and Mathematical Physics. 2019 Dec 1;9(4):2021-2031. doi: 10.1007/s13324-019-00298-7

Author

Gromadzki, G. ; Mednykh, A. D. ; Mednykh, I. A. / On automorphisms of graphs and Riemann surfaces acting with fixed points. In: Analysis and Mathematical Physics. 2019 ; Vol. 9, No. 4. pp. 2021-2031.

BibTeX

@article{8f11f9109f6742029688331a01770a20,
title = "On automorphisms of graphs and Riemann surfaces acting with fixed points",
abstract = "Let X be a finite connected graph, possibly with multiple edges. We provide each edge of the graph by two possible orientations. An automorphism group of a graph acts harmonically if it acts freely on the set of directed edges of the graph. Following M. Baker and S. Norine define a genus g of the graph X to be the rank of the first homology group. A finite group acting harmonically on a graph of genus g is a natural discrete analogue of a finite group of automorphisms acting on a Riemann surface of genus g. In the present paper, we give a sharp upper bound for the size of cyclic group acting harmonically on a graph of genus g≥ 2 with a given number of fixed points. Similar results, for closed orientable surfaces, were obtained earlier by T. Szemberg, I. Farkas and H. M. Kra.",
keywords = "Automorphism of graph, Cyclic group, Fixed point, Genus of graph, Graph covering, Graph of groups, Orbifold, Riemann surface",
author = "G. Gromadzki and Mednykh, {A. D.} and Mednykh, {I. A.}",
year = "2019",
month = dec,
day = "1",
doi = "10.1007/s13324-019-00298-7",
language = "English",
volume = "9",
pages = "2021--2031",
journal = "Analysis and Mathematical Physics",
issn = "1664-2368",
publisher = "Springer Science + Business Media",
number = "4",

}

RIS

TY - JOUR

T1 - On automorphisms of graphs and Riemann surfaces acting with fixed points

AU - Gromadzki, G.

AU - Mednykh, A. D.

AU - Mednykh, I. A.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - Let X be a finite connected graph, possibly with multiple edges. We provide each edge of the graph by two possible orientations. An automorphism group of a graph acts harmonically if it acts freely on the set of directed edges of the graph. Following M. Baker and S. Norine define a genus g of the graph X to be the rank of the first homology group. A finite group acting harmonically on a graph of genus g is a natural discrete analogue of a finite group of automorphisms acting on a Riemann surface of genus g. In the present paper, we give a sharp upper bound for the size of cyclic group acting harmonically on a graph of genus g≥ 2 with a given number of fixed points. Similar results, for closed orientable surfaces, were obtained earlier by T. Szemberg, I. Farkas and H. M. Kra.

AB - Let X be a finite connected graph, possibly with multiple edges. We provide each edge of the graph by two possible orientations. An automorphism group of a graph acts harmonically if it acts freely on the set of directed edges of the graph. Following M. Baker and S. Norine define a genus g of the graph X to be the rank of the first homology group. A finite group acting harmonically on a graph of genus g is a natural discrete analogue of a finite group of automorphisms acting on a Riemann surface of genus g. In the present paper, we give a sharp upper bound for the size of cyclic group acting harmonically on a graph of genus g≥ 2 with a given number of fixed points. Similar results, for closed orientable surfaces, were obtained earlier by T. Szemberg, I. Farkas and H. M. Kra.

KW - Automorphism of graph

KW - Cyclic group

KW - Fixed point

KW - Genus of graph

KW - Graph covering

KW - Graph of groups

KW - Orbifold

KW - Riemann surface

UR - http://www.scopus.com/inward/record.url?scp=85064687019&partnerID=8YFLogxK

U2 - 10.1007/s13324-019-00298-7

DO - 10.1007/s13324-019-00298-7

M3 - Article

AN - SCOPUS:85064687019

VL - 9

SP - 2021

EP - 2031

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

SN - 1664-2368

IS - 4

ER -

ID: 19647687