First Committee Member
Second Committee Member
Third Committee Member
graph theory, minimal edges, automorphism group, minimal vertices, dicyclic
Discrete Mathematics and Combinatorics
We find the smallest degree of a graph with automorphism group isomorphic to the dicyclic group with 4n elements, denoted α(Dic_n). We also find the fewest edges a minimum-order graph with dicyclic automorphism group and a minimal number of vertices can have. For n not a power of 2, the value of α(Dic_n) is significantly less than the best previously known upper bound, 8n. Such an edge-minimized vertex-minimal graph is constructed and shown to have automorphism group Dic_n . That the exhibited graph is minimal is verified using a combination of techniques similar to those developed previously for Abelian groups and earlier results for the special case Dic_n (where n is a power of 2).
Huston, Peter E., "On Edge-Minimization of Vertex Minimal Graphs with Dicyclic Automorphism Group" (2016). Honors Thesis Projects. Paper 31.