The Degree-Associate Reconstruction Parameters Of A Kind Of Corona Graph

The Reconstruction Conjecture was proposed by Ulam and Kelly in 1942. As one of the most important and unsolved problems in graph theory, the reconstruction conjecture asserts that every graph with at least three vertices is uniquely determined by its deck.A card is a vertex-deleted subgraph of a graph G. A dacard is an ordered pair (G - v, d(v)) that specifies the card G - v together with the degree of the deleted vertex v. The degree-associated reconstruction number drn(G) is the minimum number of dacards that determine G. The adversary degree-associated reconstruction number adrn{G) is the least k, such that every set of k dacards determines G.An edge-card is an edge-deleted subgraph of a graph G. The Edge-Reconstruction Conjecture states that every graph with more than three edges is uniquely determined by its edge-deck. A decard is an ordered pair (G - e, d(e)) which consists of the edge-card G - e together with the degree of the deleted edge e. The degree-associated edge-reconstruction number dern(G) is the minimum number of decards that determine G. The adversary degree-associated edge-reconstruction number adern(G) is the least A;, such that every set of k decards determines G.In this master thesis, we study the fundamental structure properties of the corona graph P_n(?)C_m, and determine the degree-associated reconstruction parameters and the degree-associated edge-reconstruction parameters of the corona graph P_n(?)C_m.This thesis is divided into four chapters. In the first chapter, we introduce the related concepts and the basic knowledge that involved to our thesis. Then, we give a brief survey of reconstruction number of graph. In the next chapter, we determine the degree-associated reconstruction parameters of the corona graph P_n(?)C_m. In the third chapter, we determine the degree-associated edge-reconstruction parameters of the corona graph P_n(?)C_m. In the last chapter, we summarize the results as well as the methods of this thesis, and propose some problems to be further considered.