@article {
author = {Borzooei, Rajab Ali and Shadravan, Mehrnoosh},
title = {On $l$-reconstructibility of degree list of graphs},
journal = {AUT Journal of Mathematics and Computing},
volume = {5},
number = {1},
pages = {39-44},
year = {2024},
publisher = {Amirkabir University of Technology},
issn = {2783-2449},
eissn = {2783-2287},
doi = {10.22060/ajmc.2023.21822.1112},
abstract = {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.},
keywords = {Reconstruction,$l$-Reconstructibility,degree list},
url = {https://ajmc.aut.ac.ir/article_5091.html},
eprint = {https://ajmc.aut.ac.ir/article_5091_978c2ff2b99553ff088c50d5d7dc0e25.pdf}
}