Polynomial reconstruction and terminal vertices

Abstract

The polynomial reconstruction problem (PRP) asks whether for a graph G of order at least 3, the characteristic polynomial can be reconstructed from the p-deck P D (G) of characteristic polynomials of the one-vertex-deleted subgraphs. We show that this is the case for a number of subclasses of the class of graphs with pendant edges. Moreover, we show that if the number of terminal vertices of G is sufficiently high, then G is polynomial reconstructible.