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Integral pentavalent Cayley graphs on abelian or dihedral groups

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Abstract

A graph is called integral, if all of its eigenvalues are integers. In this paper, we give some results about integral pentavalent Cayley graphs on abelian or dihedral groups.

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References

  1. Abdollahi A and Vatandoost E, Which Cayley graphs are integral? Electronic J. Combinatorics 16 (2009) #R122

    MathSciNet  MATH  Google Scholar 

  2. Abdollahi A and Vatandoost E, Integral quartic Cayley graphs abelian groups, Electronic J. Combinatorics 18 (2011) #P89

    MathSciNet  MATH  Google Scholar 

  3. Ahmadi O, Alon N, Blake I F and Shparlinski I E, Graphs with integral spectrum, Linear Algebra and its Applications 430 (2009) 547–552

    Article  MathSciNet  MATH  Google Scholar 

  4. Babai L, Spectra of Cayley graphs, J. Combinatorial Theory Ser. B 27 (1979) 180–189

    Article  MathSciNet  MATH  Google Scholar 

  5. Bussemaker F C and Cvetković D, There are exactly 13 connected, cubic, integral graphs, Univ. Beograd, Publ. Elektrotehn. Fak., Ser Mat., Fiz. 544–567 (1976) 43–48

    MathSciNet  MATH  Google Scholar 

  6. Cvetković D, Cubic integral graphs, Univ. Beograd, Publ. Elektrotehn. Fak., Ser. Mat. Fiz. 498–541 (1975) 107–113

    MathSciNet  MATH  Google Scholar 

  7. Friedman H D, On the impossibility of certain Moore graphs, J. Combin. Theory Ser. B 10 (1971) 245–252

    Article  MathSciNet  MATH  Google Scholar 

  8. Harary F and Schwenk A J, Which graphs have integral spectra? Graphs and Combinatorics 390 (1974) 45–51

    Article  MathSciNet  MATH  Google Scholar 

  9. James G and Liebeck M, Representations and Characters of Groups (1993) (Cambridge: Cambridge University Press)

    MATH  Google Scholar 

  10. Klotz W and Sander T, Some properties of unitary Cayley graphs, Electronic J. Combinatorics 14 (1) (2007) Research Paper 45, 12 pp

  11. Sander T, Sudoku graphs are integral, Electronic J. Combinatorics 16 (2009) #N25

    MathSciNet  MATH  Google Scholar 

  12. Schwenk A J, Exactly thirteen cubic graphs have integral spectra, Theory and applications of graphs (Proc. Internat. Conf., Western Mich. Univ., Kalamazoo, Mich., 1976) (1978) (Berlin: Springer) vol. 642

  13. So W, Integral circulant graphs, Discrete Math. 306 (2006) 153–158

    Article  MathSciNet  MATH  Google Scholar 

  14. Stevaović D, 4-Regular ingraphs avoiding ±3 in the spectrum, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 14 (2003) 99–110

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Urmia University, Urmia, 57135, Iran

    MOHSEN GHASEMI

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  1. MOHSEN GHASEMI
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Correspondence to MOHSEN GHASEMI.

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Communicating Editor: Sharad S Sane

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GHASEMI, M. Integral pentavalent Cayley graphs on abelian or dihedral groups. Proc Math Sci 127, 219–224 (2017). https://doi.org/10.1007/s12044-017-0332-9

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  • DOI: https://doi.org/10.1007/s12044-017-0332-9

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2000 Mathematics Subject Classification.

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