A new counting methods, including the issue of counting labelled self-complementary graphs
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Publication:5500085
zbMATH Open1321.05119arXiv0909.2314MaRDI QIDQ5500085
Publication date: 5 August 2015
Abstract: Harary and Palmer announced an enumeration problem of labelled self-complementary graphs at the end of their book (Graphical Enumeration, Academic Press, New York and London, 1973). This paper resolves this problem. A method for solving this problem leads to the derivation of following formulas: (a) A formula on the number of labelled graphs with the given order of automorphism groups of those graphs. (b) A formula on the number of unlabelled graphs with the given order of automorphism groups of those graphs. (c) A formula on the number of labelled self-complementary graphs with the given order of automorphism groups of those graphs. (d) A formula on the number of unlabelled self-complementary graphs with the given order of automorphism groups of those graphs.
Full work available at URL: https://arxiv.org/abs/0909.2314
Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)
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