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\((-1)\)-Hypomorphic Graphs with the Same 3-Element Homogeneous Subsets

  • Jamel Dammak
  • Hamza Si KaddourEmail author
Original Paper
  • 11 Downloads

Abstract

A 3-element homogeneous subset of a graph G is a 3-element subset of the vertex set of G which forms a clique or an independent set. We prove that Ulam Reconstruction Conjecture is true for pairs of graphs having the same 3-element homogeneous subsets. This new approach in graph reconstruction is motivated by a result, obtained in 2011 by Pouzet, Si Kaddour and Trotignon, giving a description of the boolean sum \(G\dot{+} G'\) of two graphs G and \(G'\) having the same 3-element homogeneous subsets.

Keywords

Graph (-1)-Hypomorphy 3-Element homogeneous subsets Boolean sum 

Mathematics Subject Classification

05C50 05C60 

Notes

Acknowledgements

We are pleased to thank the referee for his constructive comments.

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsFaculty of Sciences of SfaxSfaxTunisia
  2. 2.Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille JordanUniv LyonVilleurbanne cedexFrance

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