On the Maximal Graph of a Commutative Ring

Document Type : Original Scientific Paper


Department of Mathematics, Faculty of Science, University of Qom, Qom, I. R. Iran



Let R be a commutative ring with nonzero identity. Throughout this paper we explore some properties of two subgraphs of the maximal graph of R.


[1] D. C. Arangno, Hamiltonicity, Pancyclicity and Cycle Extendability in Graphs, PhD Thesis, Utah State University, 2014.
[2] R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory, Springer, New York, NY, USA, 2000.
[3] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, MacMillan, London, 1976.
[4] A. Gaur and A. Sharma, Maximal graph of a commutative ring, Int. J. Algebra 7 (9-12) (2013) 581 − 588.
[5] M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
[6] A. Harris, Cycle Structures in Graph, PhD Thesis, University of Colorado Denver, 2009.
[7] H. R. Maimani, M. Salimi, A. Sattari and S. Yassemi, Comaximal graph of commutative rings, J. Algebra 319 (4) (2008) 1801 − 1808.
[8] F. Mahmudi, M. Soleimani and M. H. Naderi, Some properties of the maximal graph of a commutative ring, Southeast Asian Bull. Math. 43 (2019) 525−536.
[9] P. K. Sharma and S. M. Bhatwadekar, A note on graphical representation of rings, J. Algebra 176 (1) (1995) 124 − 127.
[10] S. Visweswaran and J. Parejiya, When is the complement of the comaximal graph of a commutative ring planner?, ISRN Algebra 2014 (2014) 736043.