The only finite non-abelian groups whose commuting graph is strong 5-star free are S3, D10, A4, GA(1,5), A5, D8, Q8, D12, C4⋊C3, SL(2,3), and six groups of order 16.
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Groups with maximum vertex degree commuting graphs
The only finite non-abelian groups whose commuting graph is strong 5-star free are S3, D10, A4, GA(1,5), A5, D8, Q8, D12, C4⋊C3, SL(2,3), and six groups of order 16.