Counting unlabelled three-connected and homeomorphically irreducible two-connected graphs |
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Authors: | TRS Walsh |
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Institution: | Department of Computer Science, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 361, Canada |
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Abstract: | Recursive procedures are obtained for counting isomorphism classes of three-connected graphs and of two-connected graphs without vertices of degree 2. We apply an enumeration tool developed by R. W. Robinson to count non-isomorphic 2-connected graphs: he expressed the sums of cycle indices of automorphism groups of connected graphs in terms of those of their 2-connected components, and we do the same for 2-connected graphs and their 3-connected components. |
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