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June 2016 Enumeration of unlabeled graphs such that both the graph and its complement are 2-connected
Kumi Kobata, Shinsei Tazawa, Tomoki Yamashita
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SUT J. Math. 52(1): 41-47 (June 2016). DOI: 10.55937/sut/1468507533

Abstract

It is well-known that the complement of a disconnected graph is connected, that is, the number of disconnected unlabeled graphs whose complement is also disconnected is zero. By this fact, we can easily express the number of connected unlabeled graphs whose complement is also connected, by the numbers of graphs and connected graphs. The generating functions of them are obtained by Harary [5]. In this paper, we express the number of unlabeled graphs such that both the graph and its complement are 2-connected, by the numbers of graphs whose generating functions are known.

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Kumi Kobata. Shinsei Tazawa. Tomoki Yamashita. "Enumeration of unlabeled graphs such that both the graph and its complement are 2-connected." SUT J. Math. 52 (1) 41 - 47, June 2016. https://doi.org/10.55937/sut/1468507533

Information

Received: 28 December 2015; Revised: 15 April 2016; Published: June 2016
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1468507533

Subjects:
Primary: 05C30 , 05C40

Keywords: complement , connectivity , enumeration

Rights: Copyright © 2016 Tokyo University of Science

Vol.52 • No. 1 • June 2016
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