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Parallel enumeration of degree sequences of simple graphs. II. (English) Zbl 1293.05368
Summary: In the paper we report on the parallel enumeration of the degree sequences (their number is denoted by \(G(n)\)) and zero-free degree sequences (their number is denoted by \((G_{z}(n))\) of simple graphs on \(n = 30\) and \(n = 31\) vertices. Among others we obtained that the number of zero-free degree sequences of graphs on \(G_{z}(30) = 5 876 236 938 019 300\) and \(G_{z}(31) = 22 974 847 474 172 374\). Due to Corollary 21 in [A. Iványi et al., ibid. 3, No. 2, 230–268 (2011; Zbl 1302.05189)] these results give the number of degree sequences of simple graphs on 30 and 31 vertices.
For Part I see [A. Iványi et al., ibid. 4, No. 2, 260–288 (2012; Zbl 1305.05089)].

MSC:
05C85 Graph algorithms (graph-theoretic aspects)
68R10 Graph theory (including graph drawing) in computer science
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