Structure of graph posets for orders 4 to 8

Title: Structure of graph posets for orders 4 to 8
Creator: Adams, Peter; Eggleton, Roger B.; MacDougall, James A.
Relation: Congressus Numerantium Vol. 166, p. 63-81
Publisher: Utilitas Mathematica Publishing Co
Resource Type: journal article
Date: 2004
Description: 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 define a modified 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
Subject: graph posets
Identifier: uon:1699
Identifier: http://hdl.handle.net/1959.13/27466
Identifier: ISSN:0384-9864
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