Reconstruction Conjecture for Graphs Isomorphic to Cube of a Tree

Abstract

This paper proves the reconstruction conjecture for graphs which are isomorphic to the cube of a tree. The proof uses the reconstructibility of trees from their peripheral vertex deleted subgraphs. The main result follows from (i) characterization of the cube of a tree (ii) recognizability of the cube of a tree (iii) uniqueness of tree as a cube root of a graph G, except when G is a complete graph (iv) reconstructibility of trees from their peripheral vertex deleted subgraphs.