Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

6 Issues per year


IMPACT FACTOR 2017: 0.314
5-year IMPACT FACTOR: 0.462

CiteScore 2017: 0.46

SCImago Journal Rank (SJR) 2017: 0.339
Source Normalized Impact per Paper (SNIP) 2017: 0.845

Mathematical Citation Quotient (MCQ) 2017: 0.26

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 67, Issue 2

Issues

Zero-divisor graphs of lower dismantlable lattices I

Avinash Patil / B. N. Waphare / Vinayak Joshi / Hossein Y. Pourali
Published Online: 2017-04-28 | DOI: https://doi.org/10.1515/ms-2016-0266

Abstract

In this paper, we study the zero-divisor graphs of a subclass of dismantlable lattices. These graphs are characterized in terms of the non-ancestor graphs of rooted trees.

MSC 2010: Primary 05C25; Secondary 05C75

Keywords: dismantlable lattice; adjunct element; adjunct representation; zero-divisor graph; cover graph; incomparability graph

Dedicated to Professor N. K. Thakare on his 77th birthday

References

  • [1]

    Alizadeh, M.—Das, A. K.—Maimani, H. R.—Pournaki, M. R.—Yassemi, S.: On the diameter and girth of zero-divisor graphs of posets, Discrete Appl. Math. 160 (2012), 1319–1324.Google Scholar

  • [2]

    Anderson, D. F.—Livingston, P. S.: The zero-divisor graph of a commutative ring, J. Algebra, 217 (1999), 434–447.Web of ScienceGoogle Scholar

  • [3]

    Beck I.: Colouring of a commutative ring, J. Algebra 116 (1988), 208–226.Google Scholar

  • [4]

    Grillet, P. A.—Varlet, J. C.: Complementedness conditions in lattices, Bull. Soc. Roy. Sci. Liège 36 (1967), 628–642.Google Scholar

  • [5]

    Halaš, R.—Jukl, M.: On Beck’s colouring of posets, Discrete Math. 309 (2009), 4584–4589.Google Scholar

  • [6]

    Halaš, R.—Länger, H.: The zero divisor graph of a qoset, Order 27 (2010), 343–351.Google Scholar

  • [7]

    Joshi, V. V.: On forbidden configuration of 0-distributive lattices, Math. Bohem. 134 (2009), 59–65.Google Scholar

  • [8]

    Joshi, V. V.: Zero divisor graph of a poset with respect to an ideal, Order 29 (2012), 499–506.Web of ScienceGoogle Scholar

  • [9]

    Joshi, V. V.—Khiste, A. U.: On the zero divisor graph of a Boolean poset, Math. Slovaca 64 (2014), 511–519.Google Scholar

  • [10]

    Joshi, V. V.—Waphare, B. N.: Characterizations of 0-distributive posets. Math. Bohem. 130 (2005), 73–80.Google Scholar

  • [11]

    Joshi, V. V.—Waphare, B. N.—Pourali, H. Y.: Zero divisor graphs of lattices and primal ideals, Asian-Eur. J. Math. 5 (2012), 1250037.Google Scholar

  • [12]

    Joshi, V. V.—Waphare, B. N.—Pourali, H. Y.: On generalized zero divisor graph of a poset, Discrete Appl. Math. 161 (2013), 1490–1495.Google Scholar

  • [13]

    Kelly, D.—Rival, I.: Crowns, fences, and dismantlable lattices, Canad. J. Math. 26 (1974), 1257–1271.Google Scholar

  • [14]

    LaGrange, J. D.: Complemented zero divisor graphs and Boolean rings, J. Algebra 315 (2007), 600-611.Web of ScienceGoogle Scholar

  • [15]

    LaGrange, J. D.: On realizing zero divisor graphs, Comm. Algebra 36 (2008), 4509–4520.Web of ScienceGoogle Scholar

  • [16]

    Lu, D.—Wu, T.: The zero divisor graphs of posets and an application to semigroups, Graphs Combin. 26 (2010), 793–804.Google Scholar

  • [17]

    Nimbhorkar, S. K.—Wasadikar, M. P.—DeMeyer, L.: Coloring of semilattices, Ars Combin. 84 (2007), 97–104.Google Scholar

  • [18]

    Rival, I.: Lattices with doubly irreducible elements, Canad. Math. Bull. 17 (1974), 91–95.Google Scholar

  • [19]

    Survase, P. A.: A Study of graphs associated with lattices and related structures, Ph. D. Thesis submitted to Dr. Babasaheb Ambedkar Marathwada University, Aurangabad (MS) 2013.Google Scholar

  • [20]

    Thakare, N. K.—Pawar, M. M.—Waphare, B. N.: A structure theorem for dismantlable lattices and enumeration Period. Math. Hungar. 45 (2002), 147–160.Google Scholar

  • [21]

    West, D. B.: Introduction to Graph Theory, Second Edition, Prentice-Hall of India, New Delhi, 2002.Google Scholar

About the article

E-mail: ;


Received: 2014-10-27

Accepted: 2015-05-07

Published Online: 2017-04-28

Published in Print: 2017-04-25


Citation Information: Mathematica Slovaca, Volume 67, Issue 2, Pages 285–296, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2016-0266.

Export Citation

© 2017 Mathematical Institute Slovak Academy of Sciences.Get Permission

Comments (0)

Please log in or register to comment.
Log in