Reconstruction Conjectures in Graph Theory: A Study on its Formation and Application
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Abstract
The Reconstruction Conjecture, which states that every graph G on at least three vertices is reconstructible, is one of the most important unsolved problems in graph theory which has existed for many years. If a graph can be inferred from the collection of all of its one-vertex removed unlabeled sub graphs up to isomorphism, then it is reconstructible. In the 1980s, immense research was conducted and many meaningful results have been generated on the conundrum and its discrepancies. The last 30 years have witnessed a gradual slowing down of research work on this topic. Trees can be rebuilt, but the proof is laborious (P. J. Kelly 1957). A succinct argument was provided that uses a straightforward yet effective counting theorem and is credited to Greenwell and Hemminger (1973). This paper focuses on the formation and application of reconstruction Conjecture in graph theory. It provides an analysis of Graph theory and Lattice theory. The study discusses the methodology involved in the implementation of Graph Theory concerning Reconstruction conjectures and discusses the stages of reconstruction Conjectures. It provides a theoretical evaluation as well as a comparative analysis of reconstruction conjecturers in graph Theory. The purpose of this paper is to provide a solution to conjunctures.