On the Minimum Order of Graphs with Given Group
- 1 December 1974
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 17 (4) , 467-470
- https://doi.org/10.4153/cmb-1974-082-9
Abstract
ForGa, finite group letα(G) denote the minimum number of vertices of the graphsXthe automorphism groupA(X) of which is isomorphic toG.G. Sabidussi proved [1], thatα(G)=0(nlogd) wheren=\G\anddis the minimum number of generators ofG.As0(log n) is the best possible upper bound ford,the result established in [1] implies thatα(G)=0(nlog logn).Keywords
This publication has 2 references indexed in Scilit:
- The smallest graph whose group is cyclicCzechoslovak Mathematical Journal, 1966
- On the minimum order of graphs with given automorphism groupMonatshefte für Mathematik, 1959