On l-reconstructibility of degree list of graphs

Document Type : Original Article


Mathematics, Shahid Beheshti University, Tehran, Iran


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 (nl)-deck of a graph and the numbers of vertices with degree i for all i, nl 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 (nl)-deck of G and the numbers of vertices with degree i for all i, nl i n−3, where l ≥ 4 and n l + 6, the degree list of the graph is determined


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