The degree-associated reconstruction number of an unicentroidal tree

Borzooei, Rajab Ali; Shadravan, Mehrnoosh

doi:10.22108/toc.2024.131563.1938

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	The degree-associated reconstruction number of an unicentroidal tree
Transactions on Combinatorics
مقاله 5، دوره 14، شماره 1، خرداد 2025، صفحه 31-43 اصل مقاله (498.69 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2024.131563.1938
نویسندگان
Rajab Ali Borzooei^* ؛ Mehrnoosh Shadravan
Department of Mathematics, Shahid Beheshti University, Tehran, Iran
چکیده
As we know, by deleting one vertex of a graph $G$, we have a subgraph of $G$ called a card of $G$. Also, investigation of that each graph with at least three vertices is determined by its multiset of cards, is called the reconstruction conjecture and the minimum number of dacards that determine $G$ is denoted the degree-associated reconstruction number $drn(G)$. Barrus and West conjectured that $drn(G) \leq 2$ for all but finitely many trees. A tree is unicentroidal or bicentroidal when it has one or two centroids, respectively. An unicentroidal tree $T$ with centroid $v$ is symmetrical if for two neighbours of $u$ and $u'$ of $v$, there exists an automorphism on $T$ mapping $u$ to $u'$. In \cite{Shad}, Shadravan and Borzooei proved that the conjecture is true for any non-symmetrical unicentroidal tree. In this paper, we proved that for any symmetrical unicentroidal tree $T$, $drn(T) \leq 2$. So, we concluded that the conjecture is true for any unicentroidal tree.
کلیدواژه‌ها
Reconstruction؛ degree-associated reconstruction number؛ unicentroidal tree

مراجع
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The degree-associated reconstruction number of an unicentroidal tree