Algebraic Graph Theory Seminar - Kirti Sahu (6.3.2026)
Friday 6.13.2026 at 13:15, Lecture room M VII (online too)
Kirti Sahu (National Institute of Technology Rourkela, Odisha, India):
Minimal graphs with given automorphism groups and fixing set
Abstract:
Let G be a finite group. Define α(G) as the minimum number of vertices among all graphs Γ such that the automorphism group of Γ is isomorphic to G. For any p prime, all p-groups of order pn having cyclic subgroups of order pn −1 have been completely classified. We consider one family of groups called modular p-groups, for an odd prime p. We compute the value of α(G) for modular p-group. The fixing number of a graph Γ is defined as the smallest number of vertices in Γ that, when fixed, makes the automorphism group trivial. For a finite group G, the fixing set is defined as the set of all fixing numbers of graphs having automorphism groups isomorphic to G. We show that the fixing set of modular p-group is {1}.