Degree-associated Edge-reconstruction Parameters Of Some Trees

The Graph Reconstruction Conjecture of Ulam and Kelly has been open for more than 50 years. It asserts that every graph with at least three vertices is uniquely de-termined by its multiset of cards. Such a graph is reconstructible. Many researchers were interested in this conjecture, and obtained some results about it. Nevertheless, the conjecture remains open. Harary proposed Edge-Reconstruction Conjecture in 1964. It states that every graph with more than three edges is determined by its edge-deck.For a reconstructible graph, Harary and Plantholt introduced the reconstruction number. Myrvold proposed the adversary reconstruction number. Motivated by recon-struction questions for directed graphs, Ramachandran defined the degree-associated reconstruction number. Monikandan et al introduced the degree-associated analogue of Myrvold’s adversary concept. The definitions of edge-reconstruction can be defined similarly.In the reconstruction arguments, we obtained the upper bound by considering the possible reconstructions from a set of degree-associated edge-cards. The lower bound can be obtained by the number of common edge-cards shared by a graph with G as many as possible. Finally, we determine the degree-associated edge-reconstruction pa-rameters of double-brooms and trees with diameter 4.In this master thesis, we study two kinds of degree-associated edge-reconstruction numbers of some trees. In the first chapter, we introduce some definitions and give a brief survey of reconstruction number of graphs. In the second chapter, we determine the degree-associated edge-reconstruction parameters of double-brooms. In the third chapter, we determine the degree-associated edge-reconstruction parameters of trees with diameter 4.