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

• Jamel Dammak
Original Paper

## 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

05C50 05C60

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