English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let G be a simple graph and {1,2,…,n} be its vertex set. The polynomial reconstruction problem asks the question: given a deck P(G) containing the n characteristic polynomials of the vertex deleted subgraphs G−1, G−2, …, G−n of G, can ϕ(G,x), the characteristic polynomial of G, be reconstructed uniquely? To date, this long-standing problem has only been solved in the affirmative for some specific classes of graphs. We prove that if there exists a vertex v such that more than half of the eigenvalues of G are shared with those of G−v, then this fact is recognizable from P(G), which allows the reconstruction of ϕ(G,x). To accomplish this, we make use of determinants of certain walk matrices of G. Our main result is used, in particular, to prove that the reconstruction of the characteristic polynomial from P(G) is possible for a large subclass of disconnected graphs, strengthening a result by Sciriha and Formosa.

Graphs Having Most of Their Eigenvalues Shared by a Vertex Deleted Subgraph