Reconstruction Conjecture for Graphs Isomorphic to Cube of a Tree
Discrete Mathematics
2012-07-10 v1
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.
Keywords
Cite
@article{arxiv.1207.1875,
title = {Reconstruction Conjecture for Graphs Isomorphic to Cube of a Tree},
author = {S. K. Gupta and Akash Khandelwal},
journal= {arXiv preprint arXiv:1207.1875},
year = {2012}
}
Comments
10 pages, 2 figures