The cyclomatic number of connected graphs without solvable orbits

Karolyi, Gyula; Pal, A.

A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a non-solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c if and only if c is equal to 6, 8, 10, 11, 15, 16, 19, 20, 21, 22, or is at least 24, and briefly discuss the geometric consequences.

Additional Metadata
Keywords	graph automorphisms, cyclomatic number, solvable groups, minimal simple groups, circulant graphs, graph eigenvalues, projective algebraic curves, solvable points, solvable orbits
MSC	Graphs and abstract algebra (groups, rings, fields, etc.) (msc 05C25), Arithmetic ground fields (msc 14H25)
THEME	Logistics (theme 3)
Publisher	IHES
Series	Institut des Hautes Etudes Scientifiques preprint
Project	Spinoza prijs Lex Schrijver
Organisation	Networks and Optimization
Citation APA Style AAA Style APA Style Cell Style Chicago Style Harvard Style IEEE Style MLA Style Nature Style Vancouver Style American-Institute-of-Physics Style Council-of-Science-Editors Style BibTex Format Endnote Format RIS Format CSL Format DOIs only Format	Karolyi, G, & Pal, A. (2007). The cyclomatic number of connected graphs without solvable orbits. Institut des Hautes Etudes Scientifiques preprint. IHES.

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