# 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

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topNader 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

top- [1] M.F. Atiyah and I.G. Macdonald, Introduction to Commutative Algebra (Addison-Wesley Publishing Co, Reading, Mass.-London-Don Mills Ont, 1969).
- [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] B. Csákány and G. Pollák, The graph of subgroups of a finite group, Czechoslovak Math. J. 19 (1969) 241-247.
- [4] R.P. Grimaldi, Graphs from rings, Congr. Numer. 71 (1990) 95-103. Zbl0747.05091
- [5] E. Szpilrajn-Marczewski, Sur deux propriétés des classes d'ensembles, Fund. Math. 33 (1945) 303-307.
- [6] D.B. West, Introduction To Graph Theory (Prentice-Hall of India Pvt. Ltd, 2003).
- [7] B. Zelinka, Intersection graphs of finite abelian groups, Czechoslovak Math. J. 25 (2) (1975) 171-174. Zbl0311.05119

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