REFERENCES
- Abdollahi , A. , Akbari , S. , Maimani , H. R. ( 2006 ). Non-commuting graph of a group . Journal of Algebra 298 : 468 – 492 .
- Abdollahi , A. , Zarrin , M. ( 2010 ). Non-nilpotent graph of a group . Communications in Algebra 38 : 4390 – 4403 .
- Afkhami , M. , Farrokhi , M. , Khashyarmanesh , K. Planar ( 2014 ). Toroidal and projective commuting and non-commuting graphs. Communications in Algebra. Accepted for publication. arXiv: 1402.4978 .
- Battle , J. , Harary , F. , Kodama , Y. , Youngs , J. W. T. ( 1962 ). Additivity of the genus of a graph . Bulletin of the American Mathematical Society 68 : 565 – 568 .
- Das , A. K. , Maimani , H. R. , Pournaki , M. R. , Yassemi , S. ( 2014 ). Nonplanarity of unit graphs and classification of the toroidal ones . Pacific Journal of Mathematics 268 ( 2 ): 371 – 387 .
- Das , A. K. , Nongsiang , D. On the genus of the commuting graphs of finite non-abelian groups, arXiv:1311.6342, 2013.
- Fang , M. , Zhang , P. ( 2003 ). Finite groups with graphs containing no triangles . Journal of Algebra 264 : 613 – 619 .
- Maimani , H. R. , Wickham , C. , Yassemi , S. ( 2012 ). Rings whose total graphs have genus at most one . Rocky Mountain Journal of Mathematics 42 ( 5 ): 1551 – 1560 .
- Neumann , B. H. ( 1976 ). A problem of Paul Erdös on groups . Journal of the Australian Mathematical Society (Series A) 21 : 467 – 472 .
- Rocke , D. M. ( 1975 ). p-Groups with abelian centralizers . Proceedings of the London Mathematical Society 30 ( 3 ): 55 – 75 .
- Schmidt , R. ( 1970 ). Zentralisatorverbände endlicher gruppen . Rendiconti del Seminario Matematico della Università di Padova 44 : 97 – 131 .
- Wang , H. J. ( 2006 ). Zero-divisor graphs of genus one. Journal of Algebra 304(2): 666–678 .
- West , D. B. ( 2009 ). Introduction to Graph Theory. 2nd ed. PHI Learning Private Limited, New Delhi .
- White , A. T. (1973). Graphs, Groups and Surfaces . North-Holland Mathematics Studies, Vol. 8. New York : American Elsevier Publishing Co., Inc.
- Wickham , C. ( 2008 ). Classification of rings with genus one zero-divisor graphs . Communications in Algebra 36 ( 2 ): 325 – 345 .
- Wickham , C. ( 2009 ). Rings whose zero-divisor graphs have positive genus . Journal of Algebra 321 ( 2 ): 377 – 383 .
- Communicated by D. Macpherson.