On the intersection graphs of ideals of direct product of rings

• Autorzy: Nader Jafari Rad , Sayyed Heidar Jafari , Shamik Ghosh
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

ideal; direct sum; intersection graph; Eulerian; Hamiltonian

Kategorie tematyczne

• 05C62: Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also }
• 16D70: Structure and classification (except as in ), direct sum decomposition, cancellation
• 16D25: Ideals
• 05C75: Structural characterization of families of graphs

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2014
• Tom: 34
• Numer: 2
• Strony: 191-201

Daty

wydano

2014

otrzymano

2014-04-22

poprawiono

2014-06-04

Twórcy

autor

Nader Jafari Rad

• Department of Mathematics, Shahrood University of Technology, Shahrood, Iran

autor

Sayyed Heidar Jafari

• Department of Mathematics, Shahrood University of Technology, Shahrood, Iran

autor

Shamik Ghosh

• Department of Mathematics, Jadavpur University, Kolkata, India

Bibliografia

• [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.
• [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.
• [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.

Identyfikatory

DOI

10.7151/dmgaa.1224