A Survay on Graph Reconstruction Problem

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Moghaddasmehr, Mohammad Javad | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50349 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahmoodian, Abadoola; Daneshgar, Amir
Abstract:
The Reconstruction Conjecture asserts that every finite simple undirected graph on three or more vertices is determined, up to isomorphism, by it’s collection of vertex-deleted subgraphs. This thesis reviews the progress made on the conjecture since it was first formulated in 1941 and discusses a number of related questions. Also, we discuss the Ak property and study the A1 property where we introduce some new aspects and an alternative formulation of the conjecture itself.
Keywords:
Graphs ; Reconstruction Conjecture