On $l$-reconstructibility of degree list of graphs

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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.
Language:
English
Published:
AUT Journal of Mathematics and Computing, Volume:5 Issue: 1, Winter 2024
Pages:
39 to 44
https://www.magiran.com/p2657376  
سامانه نویسندگان
  • Rajab Ali Borzooei
    Corresponding Author (1)
    Full Professor Mathematics, Shahid Beheshti University, Tehran, Iran
    Borzooei، Rajab Ali
اطلاعات نویسنده(گان) توسط ایشان ثبت و تکمیل شده‌است. برای مشاهده مشخصات و فهرست همه مطالب، صفحه رزومه را ببینید.
مقالات دیگری از این نویسنده (گان)