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Graphs Attached to Rings Revisited

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Abstract

In this paper, we discuss some recent results on graphs attached to rings. In particular, we deal with comaximal graphs, unit graphs, and total graphs. We then define the notion of cototal graph and, using this graph, we characterize the rings which are additively generated by their zero divisors. Finally, we glance at graphs attached to other algebraic structures.

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Author information

Authors and Affiliations

  1. Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, P.O. Box 16785-163, Tehran, Iran

    H. R. Maimani

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    H. R. Maimani

  3. Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11155-9415, Tehran, Iran

    M. R. Pournaki

  4. Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran

    A. Tehranian

  5. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

    S. Yassemi

Authors
  1. H. R. Maimani
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  2. M. R. Pournaki
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  3. A. Tehranian
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  4. S. Yassemi
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Corresponding author

Correspondence to S. Yassemi.

Additional information

The research of H. R. Maimani was in part supported by a grant from IPM (No. 89050211). The research of M. R. Pournaki was in part supported by a grant from the Academy of Sciences for the Developing World (TWAS–UNESCO Associateship—Ref. FR3240126591). The research of A. Tehranian was in part supported by a grant from Islamic Azad University (IAU). The research of S. Yassemi was in part supported by a grant from the University of Tehran.

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Maimani, H.R., Pournaki, M.R., Tehranian, A. et al. Graphs Attached to Rings Revisited. Arab J Sci Eng 36, 997–1011 (2011). https://doi.org/10.1007/s13369-011-0096-y

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  • DOI: https://doi.org/10.1007/s13369-011-0096-y

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