On the intersection graphs of ideals of direct product of rings

Nader Jafari Rad; Sayyed Heidar Jafari; Shamik Ghosh

Discussiones Mathematicae - General Algebra and Applications (2014)

  • Volume: 34, Issue: 2, page 191-201
  • ISSN: 1509-9415

Abstract

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In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals of direct product of commutative rings.

How to cite

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Nader Jafari Rad, Sayyed Heidar Jafari, and Shamik Ghosh. "On the intersection graphs of ideals of direct product of rings." Discussiones Mathematicae - General Algebra and Applications 34.2 (2014): 191-201. <http://eudml.org/doc/270455>.

@article{NaderJafariRad2014,
abstract = {In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals of direct product of commutative rings.},
author = {Nader Jafari Rad, Sayyed Heidar Jafari, Shamik Ghosh},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {ideal; direct sum; intersection graph; Eulerian; Hamiltonian; zero-divisor graph; bipartite graph},
language = {eng},
number = {2},
pages = {191-201},
title = {On the intersection graphs of ideals of direct product of rings},
url = {http://eudml.org/doc/270455},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Nader Jafari Rad
AU - Sayyed Heidar Jafari
AU - Shamik Ghosh
TI - On the intersection graphs of ideals of direct product of rings
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2014
VL - 34
IS - 2
SP - 191
EP - 201
AB - In this paper we first calculate the number of vertices and edges of the intersection graph of ideals of direct product of rings and fields. Then we study Eulerianity and Hamiltonicity in the intersection graph of ideals of direct product of commutative rings.
LA - eng
KW - ideal; direct sum; intersection graph; Eulerian; Hamiltonian; zero-divisor graph; bipartite graph
UR - http://eudml.org/doc/270455
ER -

References

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  1. [1] M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra (Addison-Wesley Publishing Co, Reading, Mass.-London-Don Mills Ont, 1969). 
  2. [2] I. Chakrabarty, Sh. Ghosh, T.K. Mukherjee and M.K. Sen, Intersection graphs of ideals of rings, Discrete Math. 309 (2009) 5381-5392. doi: 10.1016/j.disc.2008.11.034. Zbl1193.05087
  3. [3] B. Csákány and G. Pollák, The graph of subgroups of a finite group, Czechoslovak Math. J. 19 (1969) 241-247. 
  4. [4] R.P. Grimaldi, Graphs from rings, Congr. Numer. 71 (1990) 95-103. Zbl0747.05091
  5. [5] E. Szpilrajn-Marczewski, Sur deux propriétés des classes d'ensembles, Fund. Math. 33 (1945) 303-307. 
  6. [6] D.B. West, Introduction To Graph Theory (Prentice-Hall of India Pvt. Ltd, 2003). 
  7. [7] B. Zelinka, Intersection graphs of finite abelian groups, Czechoslovak Math. J. 25 (2) (1975) 171-174. Zbl0311.05119

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