Reconstructing graphs from their k-edge deleted subgraphs (original) (raw)

This research addresses the problem of k-edge reconstruction in graphs, extending classical results related to edge reconstructibility. The authors demonstrate that a graph G is k-edge reconstructible if certain conditions on its edges and vertices are satisfied, particularly when comparing the number of edges to specific combinatorial factors involving vertex counts. Additionally, the analysis involves matrix representations to elucidate the relationships between different graphs based on their deleted subgraphs.