A new counting methods, including the issue of counting labelled self-complementary graphs

Shinsei Tazawa

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arXiv · 0909.2314

A new counting methods, including the issue of counting labelled self-complementary graphs

Shinsei Tazawa

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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.

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Shinsei Tazawa. 2009-09-12. A new counting methods, including the issue of counting labelled self-complementary graphs. https://arxiv.org/abs/0909.2314

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