on l-reconstructibility of degree list of graphs

The k-deck of a graph is the multiset of its subgraphs induced by k vertices which is denoted by dk(g). a graph or graph property is l-reconstructible if it is determined by the deck of subgraphs obtained by deleting l vertices. manvel proved that from the (n−l)-deck of a graph and the numbers of vertices with degree i for all i, n−l ≤ i ≤ n−1, the degree list of the graph is determined. in this paper, we extend this result and prove that if g is a graph with n vertices, then from the (n−l)-deck of g and the numbers of vertices with degree i for all i, n−l ≤ i ≤ n−3, where l ≥ 4 and n ≥ l + 6, the degree list of the graph is determined