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- W2131133612 abstract "The poset G(n) comprises the unlabelled simple graphs of order n, with partial ordering G H whenever G is a spanning subgraph of H. We dene a modifieded Steinbach numbering of the graphs in G(n), apply this numbering to each G(n) with n 8, and use it to tabulate the Hasse diagram structure of the posets with 4 n 8 together with key aspects of the independence structure of these posets. In particular, the Hasse diagram of G(8) is a directed graph of order 12346 and size 125066; the poset G(8) has 51952895 independent pairs of graphs, and 96775426396 independent triples. We present 14 tables of descriptive data for G(n) with 4 n 8. All of the underlying data can be found on our webpage www.maths.uq.edu.au/~pa/research/posets4to8.html 2000 Mathematics subject classication: primary 05C99, secondary 05C07, 06A07. Research supported by the Australian Research CThe poset G(n) comprises the unlabelled simple graphs of order n, with partial ordering G H whenever G is a spanning subgraph of H. We dene a modied Steinbach numbering of the graphs in G(n), apply this numbering to each G(n) with n 8, and use it to tabulate the Hasse diagram structure of the posets with 4 n 8 together with key aspects of the independence structure of these posets. In particular, the Hasse diagram of G(8) is a directed graph of order 12346 and size 125066; the poset G(8) has 51952895 independent pairs of graphs, and 96775426396 independent triples. We present 14 tables of descriptive data for G(n) with 4 n 8. All of the underlying data can be found on our webpage www.maths.uq.edu.au/~pa/research/posets4to8.html 2000 Mathematics subject classication: primary 05C99, secondary 05C07, 06A07." @default.
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- W2131133612 date "2004-01-01" @default.
- W2131133612 modified "2023-09-26" @default.
- W2131133612 title "Structure of graph posets for orders 4 to 8" @default.
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