The graph reconstruction number.

*(English)*Zbl 0664.05043The reconstruction number of graph G is the minimum number of point- deleted subgraphs required in order to uniquely identify the original graph G. We list, based on computer calculations, the reconstruction number for all graphs with at most seven points. Some constructions and conjectures for graphs of higher order are given. The most striking statement is our concluding conjecture that almost all graphs have reconstruction number three.

##### MSC:

05C60 | Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) |

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\textit{F. Harary} and \textit{M. Plantholt}, J. Graph Theory 9, No. 4, 451--454 (1985; Zbl 0664.05043)

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##### References:

[1] | On the reconstruction of a graph from a collection of subgraphs. Theory of Graphs and Its Applications. Academic, New York (1964), p. 47–52. |

[2] | McKay, J. Graph Theory 1 pp 281– (1977) |

[3] | A Collection of Mathematical Problems. Wiley, New York, (1960), p. 29. · Zbl 0086.24101 |

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