A Reduction of the Graph Reconstruction Conjecture

S. Monikandan; J. Balakumar

Discussiones Mathematicae Graph Theory (2014)

  • Volume: 34, Issue: 3, page 529-537
  • ISSN: 2083-5892

Abstract

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A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G) = 2 or diam(Ḡ) = diam(G) = 3 are reconstructible

How to cite

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S. Monikandan, and J. Balakumar. "A Reduction of the Graph Reconstruction Conjecture." Discussiones Mathematicae Graph Theory 34.3 (2014): 529-537. <http://eudml.org/doc/268082>.

@article{S2014,
abstract = {A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G) = 2 or diam(Ḡ) = diam(G) = 3 are reconstructible},
author = {S. Monikandan, J. Balakumar},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {reconstruction; diameter; geodetic graph; interval-regular graph},
language = {eng},
number = {3},
pages = {529-537},
title = {A Reduction of the Graph Reconstruction Conjecture},
url = {http://eudml.org/doc/268082},
volume = {34},
year = {2014},
}

TY - JOUR
AU - S. Monikandan
AU - J. Balakumar
TI - A Reduction of the Graph Reconstruction Conjecture
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 3
SP - 529
EP - 537
AB - A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G) = 2 or diam(Ḡ) = diam(G) = 3 are reconstructible
LA - eng
KW - reconstruction; diameter; geodetic graph; interval-regular graph
UR - http://eudml.org/doc/268082
ER -

References

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