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- W4320061787 abstract "The adjugate matrix of $G$, denoted by $operatorname{adj}(G)$, is the adjugate of the matrix $xmathbf{I}-mathbf{A}$, where $mathbf{A}$ is the adjacency matrix of $G$. The polynomial reconstruction problem (PRP) asks if the characteristic polynomial of a graph $G$ can always be recovered from the multiset $operatorname{mathcal{PD}}(G)$ containing the $n$ characteristic polynomials of the vertex-deleted subgraphs of $G$. Noting that the $n$ diagonal entries of $operatorname{adj}(G)$ are precisely the elements of $operatorname{mathcal{PD}}(G)$, we investigate variants of the PRP in which multisets containing entries from $operatorname{adj}(G)$ successfully reconstruct the characteristic polynomial of $G$. Furthermore, we interpret the entries off the diagonal of $operatorname{adj}(G)$ in terms of characteristic polynomials of graphs, allowing us to solve versions of the PRP that utilize alternative multisets to $operatorname{mathcal{PD}}(G)$ containing polynomials related to characteristic polynomials of graphs, rather than entries from $operatorname{adj}(G)$." @default.
- W4320061787 created "2023-02-12" @default.
- W4320061787 creator A5044655864 @default.
- W4320061787 date "2022-10-28" @default.
- W4320061787 modified "2023-09-30" @default.
- W4320061787 title "Recovering the characteristic polynomial of a graph from entries of the adjugate matrix" @default.
- W4320061787 doi "https://doi.org/10.13001/ela.2022.7231" @default.
- W4320061787 hasPublicationYear "2022" @default.
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