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On $l$-reconstructibility of degree list of graphs | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 5، دوره 5، شماره 1، 2024، صفحه 39-44 اصل مقاله (398.78 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2023.21822.1112 | ||
| نویسندگان | ||
| Rajab Ali Borzooei* ؛ Mehrnoosh Shadravan | ||
| Department of Mathematics, Shahid Beheshti University, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Reconstruction؛ $l$-Reconstructibility؛ Degree list | ||
| مراجع | ||
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