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Two Moore’s Theorems for Graphs Научная публикация

Журнал

Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
ISSN: 0049-4704

Вых. Данные

Год: 2020, Том: 52, Страницы: 469-476 Страниц : 8 DOI: 10.13137/2464-8728/30918

Ключевые слова

automorphism group; graph; harmonic action; orbifold

Авторы

Mednykh A. ^1,2 , Mednykh I. ^1,2

Организации

1	Sobolev Institute of Mathematics, pr. Koptyuga 4, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, Pirogova 1, Novosibirsk, 630090, Russian Federation

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. © 2020. All Rights Reserved.

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

Scopus:	2-s2.0-85108854523
OpenAlex:	W3200402322

БД	Цитирований
Scopus	1
OpenAlex	1