The Reconstruction of Graphs

Details The Reconstruction of Graphs The Reconstruction of Graphs

2005-03-16

arxiv.org/abs/math/0503316v2

Mathematics

General Mathematics

39 pages. Typos corrected. A new Section 17 is added which offers a new smart proof for reconstruction conjecture

Scientific paper

In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an approach to deal with reconstruction problem. We then discuss complete sets of invariants for graphs and reconstruction conjecture. We then begin with development of few equivalent formulations of reconstruction conjecture. In the last section we briefly elaborate the formulation due to Harary its exact demand and finally proceed to give a different proof of reconstruction conjecture using reconstructibility of graph from its spanning trees and reconstructibility of tree from its pendant point deleted deck of subtrees. This last proof can be used to develop a systematic procedure to reconstruct unique graph from its deck.

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