Degree associated reconstruction number of certain connected graphs with unique end vertex and a vertex of degree n−2

Abstract

A vertex-deleted subgraph of a graph [Formula: see text] is called a card of [Formula: see text] A card of [Formula: see text] with which the degree of the deleted vertex is also given is called a degree associated card (or dacard) of [Formula: see text] The degree associated reconstruction number (or drn) of a graph [Formula: see text] is the size of the smallest collection of dacards of [Formula: see text] that uniquely determines [Formula: see text] A P-graph is a graph of order [Formula: see text] with exactly two blocks, one of them has just two vertices and the other has vertex of degree [Formula: see text]. It is shown that the drn of all connected graphs of order [Formula: see text] with a unique end vertex and a vertex of degree [Formula: see text] is 1 or 2 if the drn of certain [Formula: see text]-graphs with at least two vertices of degree 2 is 2.