%0 Journal Article
%T On $l$-reconstructibility of degree list of graphs
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Borzooei, Rajab Ali
%A Shadravan, Mehrnoosh
%D 2024
%\ 01/01/2024
%V 5
%N 1
%P 39-44
%! On $l$-reconstructibility of degree list of graphs
%K Reconstruction
%K $l$-Reconstructibility
%K degree list
%R 10.22060/ajmc.2023.21822.1112
%X The $k$-deck of a graph is the multiset of its subgraphs induced by $k$ vertices which is denoted by $D_{k}(G)$. 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 $i$, $n-l \leq i \leq n-1$, 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 $i$, $n-l \leq i \leq n-3$, where $l \geq 4$ and $n \geq l+6$, the degree list of the graph is determined.
%U https://ajmc.aut.ac.ir/article_5091_978c2ff2b99553ff088c50d5d7dc0e25.pdf