On generalized zero divisor graph of a poset

被引：11
|
作者：
Joshi, Vinayak [1 ]
Waphare, B. N. [1 ]
Pourali, H. Y. [1 ]
机构：
[1] Univ Pune, Dept Math, Pune 411007, Maharashtra, India
来源：
DISCRETE APPLIED MATHEMATICS | 2013年 / 161卷 / 10-11期
关键词：
Zero divisor graph; Clique number; Chromatic number; r-partite graph; Semi-ideal; Ideal; Prime ideal; Semiprime ideal; IDEALS;
D O I：
10.1016/j.dam.2012.12.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce the generalized ideal based zero divisor graph of a poset P, denoted by <(G(I)(P))over cap>. A representation theorem is obtained for generalized zero divisor graphs. It is proved that a graph is complete r-partite with r >= 2 if and only if it is a generalized zero divisor graph of a poset. As a consequence of this result, we prove a form of a Beck's Conjecture for generalized zero divisor graphs of a poset. Further, it is proved that a generalized zero divisor graph <(G({0})(P))over cap> of a section semi-complemented poset P with respect to the ideal (0] is a complete graph. (C) 2013 Elsevier By. All rights reserved.
引用
收藏
页码：1490 / 1495
页数：6
相关论文
共 50 条
  • [41] The maximal degree of a zero-divisor graph
    Mohammad, Husam Q.
    Shuker, Nazar H.
    Khaleel, Luma A.
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2021, 14 (01)
  • [42] Zero-divisor graph of C(X)
    F. Azarpanah
    M. Motamedi
    Acta Mathematica Hungarica, 2005, 108 : 25 - 36
  • [43] ZERO DIVISOR GRAPHS OF LATTICES AND PRIMAL IDEALS
    Joshi, Vinayak
    Waphare, B. N.
    Pourali, H. Y.
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2012, 5 (03)
  • [44] INTERVALS OF POSETS OF A ZERO-DIVISOR GRAPH
    Lagrange, John D.
    MATHEMATICA SLOVACA, 2024, 74 (04) : 803 - 818
  • [45] Radio Number Associated with Zero Divisor Graph
    Koam, Ali N. A.
    Ahmad, Ali
    Haider, Azeem
    MATHEMATICS, 2020, 8 (12) : 1 - 10
  • [46] FUZZY ZERO DIVISOR GRAPH IN A COMMUTATIVE RING
    Kuppan, A.
    Sankar, J. Ravi
    TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2021, 11 : 42 - 50
  • [47] On the metric dimension of a zero-divisor graph
    Pirzada, S.
    Raja, Rameez
    COMMUNICATIONS IN ALGEBRA, 2017, 45 (04) : 1399 - 1408
  • [48] Zero-divisor graph and comaximal graph of rings of continuous functions with countable range
    Bharati, Rakesh
    Acharyya, Amrita
    Ray, A. Deb
    Acharyya, Sudip Kumar
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024, 23 (14)
  • [49] On the diameter of the zero-divisor graph over skew PBW extensions
    Abdi, M.
    Talebi, Y.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024, 23 (05)
  • [50] Cliques in the extended zero-divisor graph of finite commutative rings
    Pirzada, Shariefuddin
    Altaf, Aaqib
    COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2025, 10 (01) : 195 - 206
12345