On the Oikawa and Arakawa Theorems for Graphs

Mednykh, Alexander; Mednykh, I. A.; Nedela, Roman

doi:10.1134/s0081543819020147

Search citation statements

Order By: Relevance

Paper Sections

Select...

Further Definitions and Basic Results1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2019

2021

Publication Types

Select...

Other2

Article1

Relationship

Self Cite1

Independent2

Authors

Journals

Cited by 3 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 13. If for every vertex u ∈ V(∆) there exist a constant c u such that λ(x) = c u for every dart x ∈ ∆(u), then the generalised covering projection ϕ : Γ → ∆ is a branched covering as defined [20,21].…”

Section: Further Definitions and Basic Resultsmentioning

confidence: 99%

Generalised Voltage Graphs

Potočnik¹,

Toledo²

2019

Preprint

View full text Add to dashboard Cite

A graph with a semiregular group of automorphisms can be thought of as the derived cover arising from a voltage graph. Since its inception, the theory of voltage graphs and their derived covers has been a powerful tool used in the study of graphs with a significant degree of symmetry. We generalise this theory to graphs with a group of automorphisms that is not necessarily semiregular, and we generalise several well-known results of the classical theory of voltage graphs to this broader setting.

show abstract

Section: Further Definitions and Basic Resultsmentioning

confidence: 99%

Generalised Voltage Graphs

Potočnik¹,

Toledo²

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…In papers [2,3], a discrete version of the classical 84(g − 1) Hurwitz theorem is established. Discrete versions of the Oikawa and the Arakawa theorems that rene the Hurwitz theorem for various classes of groups were obtained in [5].…”

Section: Introductionmentioning

confidence: 99%

Fixed points of cyclic groups acting purely harmonically on a graph

Mednykh¹

2021

Sib. Elektron. Mat. Izv.

Self Cite

View full text Add to dashboard Cite

Let X be a nite 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. Dene a genus g of the graph X to be the rank of the rst 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 xed points has an automorphism generating a ¾large¿ cyclic group Zn of order n ≥ 2g − 1. We show that in the most cases, the automorphism acts xed point free, while for groups of order 2g and 2g − 1 it can have one or two xed points.

show abstract

Two Moore's theorems for graphs

Mednykh¹,

Mednykh

2020

View full text Add to dashboard Cite

On the Oikawa and Arakawa Theorems for Graphs

Cited by 3 publications

References 9 publications

Generalised Voltage Graphs

Generalised Voltage Graphs

Fixed points of cyclic groups acting purely harmonically on a graph

Two Moore's theorems for graphs

Contact Info

Product

Resources

About