Two Moore’s Theorems for Graphs

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Two Moore’s Theorems for Graphs. / Mednykh, Alexander ; Mednykh, Ilya.

In: Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, Vol. 52, 2020, p. 469-476.

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

Harvard

Mednykh, A & Mednykh, I 2020, 'Two Moore’s Theorems for Graphs', Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, vol. 52, pp. 469-476. https://doi.org/10.13137/2464-8728/30918

APA

Mednykh, A., & Mednykh, I. (2020). Two Moore’s Theorems for Graphs. Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, 52, 469-476. https://doi.org/10.13137/2464-8728/30918

Vancouver

Mednykh A , Mednykh I. Two Moore’s Theorems for Graphs. Rendiconti dell'Istituto di Matematica dell'Universita di Trieste. 2020;52:469-476. doi: 10.13137/2464-8728/30918

Author

Mednykh, Alexander ; Mednykh, Ilya. / Two Moore’s Theorems for Graphs. In: Rendiconti dell'Istituto di Matematica dell'Universita di Trieste. 2020 ; Vol. 52. pp. 469-476.

BibTeX

@article{cf13bb1274304d91a7e7d4f1302bdef1,

title = "Two Moore{\textquoteright}s Theorems for Graphs",

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 invert-ible edges. Define a genus g of the graph X to be the rank of the first homology group. A finite group acting purely harmonically on a graph of genus g is a natural discrete analogue of a finite group of automor-phisms acting on a Riemann surface of genus g. In the present paper, we investigate cyclic group (Formula presented)nacting purely harmonically on a graph X of genus g with fixed points. Given subgroup (Formula presented)d< (Formula presented)n, we find the signature of orbifold X/(Formula presented)dthrough the signature of orbifold X/(Formula presented)n. As a result, we obtain formulas for the number of fixed points for generators of group (Formula presented)dand for genus of orbifold X/(Formula presented)d. For Riemann surfaces, similar results were obtained earlier by M. J. Moore.",

keywords = "automorphism group, graph, harmonic action, orbifold",

author = "Alexander Mednykh and Ilya Mednykh",

year = "2020",

doi = "10.13137/2464-8728/30918",

language = "English",

volume = "52",

pages = "469--476",

journal = "Rendiconti dell'Istituto di Matematica dell'Universita di Trieste",

issn = "0049-4704",

publisher = "Istituto di matematica, Universita di Trieste",

}

RIS

TY - JOUR

T1 - Two Moore’s Theorems for Graphs

AU - Mednykh, Alexander

AU - Mednykh, Ilya

PY - 2020

Y1 - 2020

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 invert-ible edges. Define a genus g of the graph X to be the rank of the first homology group. A finite group acting purely harmonically on a graph of genus g is a natural discrete analogue of a finite group of automor-phisms acting on a Riemann surface of genus g. In the present paper, we investigate cyclic group (Formula presented)nacting purely harmonically on a graph X of genus g with fixed points. Given subgroup (Formula presented)d< (Formula presented)n, we find the signature of orbifold X/(Formula presented)dthrough the signature of orbifold X/(Formula presented)n. As a result, we obtain formulas for the number of fixed points for generators of group (Formula presented)dand for genus of orbifold X/(Formula presented)d. For Riemann surfaces, similar results were obtained earlier by M. J. Moore.

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 invert-ible edges. Define a genus g of the graph X to be the rank of the first homology group. A finite group acting purely harmonically on a graph of genus g is a natural discrete analogue of a finite group of automor-phisms acting on a Riemann surface of genus g. In the present paper, we investigate cyclic group (Formula presented)nacting purely harmonically on a graph X of genus g with fixed points. Given subgroup (Formula presented)d< (Formula presented)n, we find the signature of orbifold X/(Formula presented)dthrough the signature of orbifold X/(Formula presented)n. As a result, we obtain formulas for the number of fixed points for generators of group (Formula presented)dand for genus of orbifold X/(Formula presented)d. For Riemann surfaces, similar results were obtained earlier by M. J. Moore.

KW - automorphism group

KW - graph

KW - harmonic action

KW - orbifold

UR - http://www.scopus.com/inward/record.url?scp=85108854523&partnerID=8YFLogxK

U2 - 10.13137/2464-8728/30918

DO - 10.13137/2464-8728/30918

M3 - Article

AN - SCOPUS:85108854523

VL - 52

SP - 469

EP - 476

JO - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

JF - Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

SN - 0049-4704

ER -

ID: 34097028