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On the automorphism group of polyhedral graphs. (English) Zbl 1410.05086

Summary: A \((4,6)\)-fullerene is a three connected cubic planar graph whose faces are squares and hexagons. In this paper, for a given \((4,6)\)-fullerene graph \(F\), we compute the order of automorphism group \(F\). We also study some spectral properties of fullerene graphs via their automorphism group.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
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