Smallest graphs with given automorphism group
Danai Deligeorgaki

TL;DR
This paper investigates the minimal size of graphs with a given automorphism group, establishing upper bounds and computing exact values for specific groups, advancing understanding of graph symmetries.
Contribution
It proves an upper bound on the smallest graph size for a given automorphism group, identifies exceptions, and computes exact values for previously unknown cases.
Findings
Proved that lpha(G) |G| with specific exceptions.
Identified four infinite families and 17 small groups as exceptions.
Computed lpha(G) for groups where the value was previously unknown.
Abstract
For a finite group , denote by the minimum number of vertices of any graph having . In this paper, we prove that , with specified exceptions. The exceptions include four infinite families of groups, and 17 other small groups. Additionally, we compute for the groups such that where the value was previously unknown.
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