I have a paper on the Reconstruction Conjecture. It was published in an Elsevier journal dedicated to Discrete mathematicsMathematics. Its available online since 2007. It's titled "Note: The Reconstruction Conjecture and edge ideals".Its at sciencedirect.com. I do not have the exact link, so I guess you'll have to search it. The Authors are Kia Dalili, Sara Faridi and Will Traves.
Kia Dalili, Sara Faridi and Will Traves. Note: The Reconstruction Conjecture and edge ideals. Discrete Mathematics 308(10), pp. 2002–2010, 2008. (MathSciNet review)
Just type Kia Dalili in the Author field for Search and it will show up.