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Mathematica Slovaca

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Volume 68, Issue 1

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Zero-divisor graphs of lower dismantlable lattices II

Avinash Patil / B. N. Waphare
  • Department of Mathematics, Center for Advanced Study in Mathematics, Savitribai Phule Pune University, Pune-411007, India
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/ Vinayak Joshi
  • Department of Mathematics, Center for Advanced Study in Mathematics, Savitribai Phule Pune University, Pune-411007, India
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Published Online: 2018-02-09 | DOI: https://doi.org/10.1515/ms-2017-0095

Abstract

In this paper, we continue our study of the zero-divisor graphs of lower dismantlable lattices that was started in [PATIL, A.—WAPHARE, B. N.—JOSHI, V.—POURALI, H. Y.: Zero-divisor graphs of lower dismantlable lattices I, Math. Slovaca 67 (2017), 285–296]. The present paper mainly deals with an Isomorphism Problem for the zero-divisor graphs of lattices. In fact, we prove that the zero-divisor graphs of lower dismantlable lattices with the greatest element 1 as join-reducible are isomorphic if and only if the lattices are isomorphic.

MSC 2010: Primary 05C60; Secondary 05C25

Keywords: dismantlable lattice; adjunct element; zero-divisor graph; rooted tree

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About the article

,


Received: 2015-09-15

Accepted: 2016-09-16

Published Online: 2018-02-09

Published in Print: 2018-02-23


Citation Information: Mathematica Slovaca, Volume 68, Issue 1, Pages 225–238, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0095.

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