Number of the records: 1
On Wiman's theorem for graphs
- Mednykh, Alexander, 1953-
On Wiman's theorem for graphs / Alexander Mednykh, Ilya Mednykh. -- © 2015 Elsevier B.V.Abstract The aim of the paper is to find discrete versions of the Wiman theorem which states that the maximum possible order of an automorphism of a Riemann surface of genus g≥2 is 4g+2. The role of a Riemann surface in this paper is played by a finite connected graph. The genus of a graph is defined as the rank of its homology group. Let ZinfN/inf be a cyclic group acting freely on the set of directed edges of a graph X of genus g≥2. We prove that N≤2g+2. The upper bound N=2g+2 is attained for any even g. In this case, the signature of the orbifold X/ZinfN/inf is (0;2,g+1), that is X/ZinfN/inf is a tree with two branch points of order 2 and g+1 respectively. Moreover, if N<2g+2, then N≤2g. The upper bound N=2g is attained for any g≥2. The latter takes a place when the signature of the orbifold X/ZinfN/inf is (0;2,2g).
In Discrete Mathematics. -- Amsterdam : Elsevier B.V., 2015. -- ISSN 0012-365X. -- ISSN 1872-681X. -- Vol. 338, no. 10 special issue (2015), pp. 1793-1800
Number of the records: 1