Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647221 | Discrete Mathematics | 2015 | 9 Pages |
Abstract
This paper studies groups of maximal size acting harmonically on a finite graph. Our main result states that these maximal graph groups are exactly the finite quotients of the modular group Γ=〈x,y∣x2=y3=1〉Γ=〈x,y∣x2=y3=1〉 of size at least 6. This characterization may be viewed as a discrete analogue of the description of Hurwitz groups as finite quotients of the (2,3,7)(2,3,7)-triangle group in the context of holomorphic group actions on Riemann surfaces. In fact, as an immediate consequence of our result, every Hurwitz group is a maximal graph group, and the final section of the paper establishes a direct connection between maximal graphs and Hurwitz surfaces via the theory of combinatorial maps.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Scott Corry,