PROJECTIVE TOTAL GRAPHS OF COMMUTATIVE RINGS

被引：8
|
作者：
Khashyarmanesh, Kazem [1 ]
Khorsandi, Mahdi Reza [1 ]
机构：
[1] Ferdowsi Univ Mashhad, Dept Pure Math, Mashhad, Iran
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2013年 / 43卷 / 04期
关键词：
Total graph; projective graph; crosscap number; zerodivisor graph; ZERO-DIVISOR GRAPH; GENUS; CLASSIFICATION; PLANAR;
D O I：
10.1216/RMJ-2013-43-4-1207
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let T(Gamma(R)) be the total graph of a commutative ring R, that is, a graph with all elements of R as vertices and two distinct vertices a and b are adjacent if and only if a + b is a zero-divisor on R. In this paper, we classify all finite rings R whose total graphs T(Gamma(R)) are projective.
引用
收藏
页码：1207 / 1213
页数：7
相关论文
共 50 条
  • [31] ON GRAPHS ASSOCIATED WITH MODULES OVER COMMUTATIVE RINGS
    Pirzada, Shariefuddin
    Raja, Rameez
    [J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2016, 53 (05) : 1167 - 1182
  • [32] The metric dimension of annihilator graphs of commutative rings
    Soleymanivarniab, V
    Tehranian, A.
    Nikandish, R.
    [J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (05)
  • [33] The Square Mapping Graphs of Finite Commutative Rings
    Wei, Yangjiang
    Tang, Gaohua
    Su, Huadong
    [J]. ALGEBRA COLLOQUIUM, 2012, 19 (03) : 569 - 580
  • [34] Toroidality of Intersection Graphs of Ideals of Commutative Rings
    Zoran S. Pucanović
    Zoran Z. Petrović
    [J]. Graphs and Combinatorics, 2014, 30 : 707 - 716
  • [35] Perfect unit graphs of commutative Artinian rings
    Mirghadim, S. M. Saadat
    Nikandish, R.
    Nikmehr, M. J.
    [J]. AFRIKA MATEMATIKA, 2021, 32 (5-6) : 891 - 896
  • [36] Generalized Cayley graphs associated to commutative rings
    Afkhami, Mojgan
    Khashyarmanesh, Kazem
    Nafar, Khosro
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 437 (03) : 1040 - 1049
  • [37] Perfect unit graphs of commutative Artinian rings
    S. M. Saadat Mirghadim
    R. Nikandish
    M. J. Nikmehr
    [J]. Afrika Matematika, 2021, 32 : 891 - 896
  • [38] Toroidality of Intersection Graphs of Ideals of Commutative Rings
    Pucanovic, Zoran S.
    Petrovic, Zoran Z.
    [J]. GRAPHS AND COMBINATORICS, 2014, 30 (03) : 707 - 716
  • [39] The Total Graphs of Finite Commutative Semirings
    David Dolžan
    Polona Oblak
    [J]. Results in Mathematics, 2017, 72 : 193 - 204
  • [40] The Total Graphs of Finite Commutative Semirings
    Dolzan, David
    Oblak, Polona
    [J]. RESULTS IN MATHEMATICS, 2017, 72 (1-2) : 193 - 204
12345