Counting classes of labeled 2-connected graphs
Pootheri, Sridar Kuttan
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Applying the Tutte decomposition of 2-connected graphys into 3-block trees, unique structural characterizations of several classes of 2-connected graphs were provided in the PhD dissertation of the author under the title "Characterizing and counting classes of unlabeled 2-connected graphs". In this thesis counting equations are derived for labeled minimally 2-connected graphs, labeled 2-connected minimally 2-edge-connected graphs and labeled 2-connected 3-edge-connected graphs based on these structural relations. The appendices contain tables of the numbers of these three classes of 2-connected graphs, by number of nodes and number of edges, obtained by computer implementation of the counting equations. These are listed for node orderes up to 34, 21 and 34 respectively. Also tables of the numbers of labeled 3-edge-connected and minimally 2-edge-connected graphys (not necessarily 2-connected) are included for node orders up to 21 and 34.
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Pootheri, Sridar Kuttan (uga, 2000-05)Applying the Tutte decomposition of 2-connected graphs into 3-block trees we provide unique structural characterizations of several classes of 2-connected graphs, including minimally 2-connected graphs, minimally ...
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