Research Article
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Monojenik yarıgrup graflarının güçlü çarpımlarının bazı graf parametreleri

Year 2018, Volume: 20 Issue: 1, 412 - 420, 25.04.2018
https://doi.org/10.25092/baunfbed.418449

Abstract

Das ve diğ. (2013) çalışmasında monojenik
yarıgruplar üzerinde yeni bir cebirsel graf tanımlanmıştır. Bu çalışmada ana
odaklanma noktamız, bu çalışmayı verilen özel cebirsel grafların güçlü
çarpımına genişletmektir. Detaylandıracak olursak, herhangi iki monojenik
yarıgrup graflarının güçlü çarpımları için bazı önemli graf parametrelerini
(çap, çevrim, yarıçap, maksimum derece, minimum derece, renklendirme sayısı,
klik sayısı ve baskınlık sayısı) hesaplayacağız.

References

  • Das, K.C., Akgunes, N. and Cevik, A.S. On a graph of monogenic semigroup, Journal of Inequalities and Application, 2013, 44, 1-13, (2013).
  • Beck, I., Coloring of commutating ring, Journal of Algebra, 116, 208-226, (1988).
  • Anderson, D.F. and Livingston, P.S., The zero-divisor graph of commutative ring, Journal of Algebra, 217, 434-447, (1999).
  • Anderson, D.F. and Badawi, A., On the zero-divisor graph of a ring, Communications in Algebra, 36, 8, 3073-3092, (2008).
  • Anderson, D.D. and Naseer, M., Beck’s coloring of a commutative ring, Journal of Algebra, 159, 500-514, (1991).
  • DeMeyer, F.R. and DeMeyer, L., Zero-divisor graphs of semigroups, Journal of Algebra, 283, 190-198, (2005).
  • DeMeyer, F.R., McKenzie, T. and Schneider, K., The zero-divisor graph of a commutative semigroup, Semigroup Forum, 65, 206-214, (2002).
  • Doŝlić, T., Ghorbani, M. and Hosseinzadeh, M.A., The relationships between wiener index, stability number and clique number of composite graphs, Bulletin of Malaysian Mathematical Sciences Society, 36, 1, 165–172, (2013).
  • Hammack, R., Imrich W. and Klavžar, S., Handbook of product graphs, Second Edition (CRC Press, Boca Raton, FL, 2011).
  • Imrich, W., Factoring cardinal product graphs in polynomial time discrete metric spaces (Villeurbanne, 1996), Discrete Mathematics, 192, 1, 119-144, (1998).
  • Imrich, W. and Klavžar, S., Product graphs. structure and recognition, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience, New York, xvi+358, (2000).
  • Klavžar, S., Coloring graph products – a survey, Discrete Mathematics 155, 135-145, (1996).
  • Yeh, Y.N. and Gutman, I., On the sum of all distances in composite graphs, Discrete Mathematics, 135, 359–365, (1994).
  • Žerovnik, J., Chromatic numbers of the strong product of odd cycles, Mathematica Slovaca 56, 4, 379–385, (2006).

Some graph parameters on the strong product of monogenic semigroup graphs

Year 2018, Volume: 20 Issue: 1, 412 - 420, 25.04.2018
https://doi.org/10.25092/baunfbed.418449

Abstract

In Das et al. (2013), it
has been defined a new algebraic graph on monogenic semigroups. Our main scope
in this study, is to extend this study over the special algebraic graphs to the
strong product. In detail, we will determinate some important graph parameters
(diameter, girth, radius, maximum degree, minimum degree, chromatic number,
clique number and domination number) for the strong product of any two monogenic
semigroup graphs.

References

  • Das, K.C., Akgunes, N. and Cevik, A.S. On a graph of monogenic semigroup, Journal of Inequalities and Application, 2013, 44, 1-13, (2013).
  • Beck, I., Coloring of commutating ring, Journal of Algebra, 116, 208-226, (1988).
  • Anderson, D.F. and Livingston, P.S., The zero-divisor graph of commutative ring, Journal of Algebra, 217, 434-447, (1999).
  • Anderson, D.F. and Badawi, A., On the zero-divisor graph of a ring, Communications in Algebra, 36, 8, 3073-3092, (2008).
  • Anderson, D.D. and Naseer, M., Beck’s coloring of a commutative ring, Journal of Algebra, 159, 500-514, (1991).
  • DeMeyer, F.R. and DeMeyer, L., Zero-divisor graphs of semigroups, Journal of Algebra, 283, 190-198, (2005).
  • DeMeyer, F.R., McKenzie, T. and Schneider, K., The zero-divisor graph of a commutative semigroup, Semigroup Forum, 65, 206-214, (2002).
  • Doŝlić, T., Ghorbani, M. and Hosseinzadeh, M.A., The relationships between wiener index, stability number and clique number of composite graphs, Bulletin of Malaysian Mathematical Sciences Society, 36, 1, 165–172, (2013).
  • Hammack, R., Imrich W. and Klavžar, S., Handbook of product graphs, Second Edition (CRC Press, Boca Raton, FL, 2011).
  • Imrich, W., Factoring cardinal product graphs in polynomial time discrete metric spaces (Villeurbanne, 1996), Discrete Mathematics, 192, 1, 119-144, (1998).
  • Imrich, W. and Klavžar, S., Product graphs. structure and recognition, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience, New York, xvi+358, (2000).
  • Klavžar, S., Coloring graph products – a survey, Discrete Mathematics 155, 135-145, (1996).
  • Yeh, Y.N. and Gutman, I., On the sum of all distances in composite graphs, Discrete Mathematics, 135, 359–365, (1994).
  • Žerovnik, J., Chromatic numbers of the strong product of odd cycles, Mathematica Slovaca 56, 4, 379–385, (2006).
There are 14 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Nihat Akgüneş

Submission Date February 2, 2018
Publication Date April 25, 2018
Published in Issue Year 2018 Volume: 20 Issue: 1

Cite

APA Akgüneş, N. (2018). Some graph parameters on the strong product of monogenic semigroup graphs. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(1), 412-420. https://doi.org/10.25092/baunfbed.418449
AMA Akgüneş N. Some graph parameters on the strong product of monogenic semigroup graphs. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi. July 2018;20(1):412-420. doi:10.25092/baunfbed.418449
Chicago Akgüneş, Nihat. “Some Graph Parameters on the Strong Product of Monogenic Semigroup Graphs”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20, no. 1 (July 2018): 412-20. https://doi.org/10.25092/baunfbed.418449.
EndNote Akgüneş N (July 1, 2018) Some graph parameters on the strong product of monogenic semigroup graphs. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 1 412–420.
IEEE N. Akgüneş, “Some graph parameters on the strong product of monogenic semigroup graphs”, Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 20, no. 1, pp. 412–420, 2018, doi: 10.25092/baunfbed.418449.
ISNAD Akgüneş, Nihat. “Some Graph Parameters on the Strong Product of Monogenic Semigroup Graphs”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20/1 (July2018), 412-420. https://doi.org/10.25092/baunfbed.418449.
JAMA Akgüneş N. Some graph parameters on the strong product of monogenic semigroup graphs. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2018;20:412–420.
MLA Akgüneş, Nihat. “Some Graph Parameters on the Strong Product of Monogenic Semigroup Graphs”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 20, no. 1, 2018, pp. 412-20, doi:10.25092/baunfbed.418449.
Vancouver Akgüneş N. Some graph parameters on the strong product of monogenic semigroup graphs. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2018;20(1):412-20.