Degree associated reconstruction number of connected digraphs with unique end vertex

A vertex-deleted unlabeled subdigraph of a digraph D is a card of D. A dacard specifies the degree triple (a, b, c) of the deleted vertex along with the card, where a and b are respectively the indegree and outdegree of v and c is the number of symmetric pairs of arcs (each pair considered as unordered edge) incident with v. The degree (triple) associated reconstruction number, drn(D), of a digraph D is the size of the smallest collection of dacards of D that uniquely determines D. A P-digraph is a connected digraph of order p ≥ 4 with exactly two blocks; only one of them has just two vertices and the other block has a vertex of degree triple (0, 0, p− 2) other than the cutvertex. In this paper, we prove that the drn is at most 3 for all P -digraphs except one type and show that the drn of all connected digraphs D, with a unique end vertex in D and an end vertex in D, is at most max{3, k} if the drn of the exceptional type of P-digraphs is at most k for some k.