Research Article
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Year 2021, , 57 - 62, 30.06.2021
https://doi.org/10.47000/tjmcs.756323

Abstract

References

  • [1] Akgunes, N., Das, K.C., Cevik, A.S., Cangul, I.N., Some properties on the lexicographic product of graphs obtained by monogenic semigroups, J. Inequal. Appl., 238(2013), 1–9.
  • [2] Akgunes, N., Das, K. Ch., Cevik, A.S., Some properties on the tensor product of graphs obtained by monogenic semigroups, Appl. Math. Comput., 235(2014), 352–357.
  • [3] Anderson, D.F., Livingston, P.S., The zero-divisor graph of commutative ring, Journal of Algebra, 217(1999), 434–447.
  • [4] Anderson, D.F., Badawi, A., On the zero-divisor graph of a ring, Comm. Algebra, 36(2008), 3073–3092.
  • [5] Anderson, D.D., Naseer, M., Beck’s coloring of a commutative ring, Journal of Algebra, 159(1991), 500–514.
  • [6] Beck, I., Coloring of commutating ring, Journal of Algebra, 116(1988), 208–226.
  • [7] Das, K.C., Akgunes, N., Cevik, A.S., On a graph of monogenic semigroup, Journal of Ineq.and Appl., 44(2013), 1–13.
  • [8] DeMeyer, F.R., McKenzie, T., Schneider, K., The zero-divisor graph of a commutative semigroup, Semigroup Forum, 65(2002), 206–214.
  • [9] DeMeyer, F.R., DeMeyer, L., Zero-divisor graphs of semigroups, Journal of Algebra, 283(2005), 190–198.
  • [10] Gross, J.L., Yellen, J., Handbook of graph theory, Chapman Hall, CRC Press 2004.
  • [11] Klavzar, S., Coloring graph products - a survey, Discrete Math., 155(1996), 135–145.
  • [12] Mukwembi, S., A note on diameter and the degree sequence of a graph, Appl. Math. Lett., 25(2002), 175–178.
  • [13] Nacaroglu, Y., On the corona product of monogenic semigroup graphs, Adv. and Appl. in Discrete Math., 19(2018), 409–420.
  • [14] Nacaroglu, Y., Akgunes, N., On the sigma index of the corona products of monogenic semigroup graphs, JUM., 2 (1)(2019), 68–74.

On Join Operation of Graphs by Obtained Monogenic Semigroups

Year 2021, , 57 - 62, 30.06.2021
https://doi.org/10.47000/tjmcs.756323

Abstract

For each commutative ring $R$ we associate a simple graph $\Gamma(R)$. This relationship presents a link between algebra and graph theory. Our main scope in this study is to extend this study over the special algebraic graphs to join graph operations. In this paper, we will give some graph parameters for the join of monogenic semigroup graphs.

References

  • [1] Akgunes, N., Das, K.C., Cevik, A.S., Cangul, I.N., Some properties on the lexicographic product of graphs obtained by monogenic semigroups, J. Inequal. Appl., 238(2013), 1–9.
  • [2] Akgunes, N., Das, K. Ch., Cevik, A.S., Some properties on the tensor product of graphs obtained by monogenic semigroups, Appl. Math. Comput., 235(2014), 352–357.
  • [3] Anderson, D.F., Livingston, P.S., The zero-divisor graph of commutative ring, Journal of Algebra, 217(1999), 434–447.
  • [4] Anderson, D.F., Badawi, A., On the zero-divisor graph of a ring, Comm. Algebra, 36(2008), 3073–3092.
  • [5] Anderson, D.D., Naseer, M., Beck’s coloring of a commutative ring, Journal of Algebra, 159(1991), 500–514.
  • [6] Beck, I., Coloring of commutating ring, Journal of Algebra, 116(1988), 208–226.
  • [7] Das, K.C., Akgunes, N., Cevik, A.S., On a graph of monogenic semigroup, Journal of Ineq.and Appl., 44(2013), 1–13.
  • [8] DeMeyer, F.R., McKenzie, T., Schneider, K., The zero-divisor graph of a commutative semigroup, Semigroup Forum, 65(2002), 206–214.
  • [9] DeMeyer, F.R., DeMeyer, L., Zero-divisor graphs of semigroups, Journal of Algebra, 283(2005), 190–198.
  • [10] Gross, J.L., Yellen, J., Handbook of graph theory, Chapman Hall, CRC Press 2004.
  • [11] Klavzar, S., Coloring graph products - a survey, Discrete Math., 155(1996), 135–145.
  • [12] Mukwembi, S., A note on diameter and the degree sequence of a graph, Appl. Math. Lett., 25(2002), 175–178.
  • [13] Nacaroglu, Y., On the corona product of monogenic semigroup graphs, Adv. and Appl. in Discrete Math., 19(2018), 409–420.
  • [14] Nacaroglu, Y., Akgunes, N., On the sigma index of the corona products of monogenic semigroup graphs, JUM., 2 (1)(2019), 68–74.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Yaşar Nacaroğlu 0000-0001-7179-0490

Publication Date June 30, 2021
Published in Issue Year 2021

Cite

APA Nacaroğlu, Y. (2021). On Join Operation of Graphs by Obtained Monogenic Semigroups. Turkish Journal of Mathematics and Computer Science, 13(1), 57-62. https://doi.org/10.47000/tjmcs.756323
AMA Nacaroğlu Y. On Join Operation of Graphs by Obtained Monogenic Semigroups. TJMCS. June 2021;13(1):57-62. doi:10.47000/tjmcs.756323
Chicago Nacaroğlu, Yaşar. “On Join Operation of Graphs by Obtained Monogenic Semigroups”. Turkish Journal of Mathematics and Computer Science 13, no. 1 (June 2021): 57-62. https://doi.org/10.47000/tjmcs.756323.
EndNote Nacaroğlu Y (June 1, 2021) On Join Operation of Graphs by Obtained Monogenic Semigroups. Turkish Journal of Mathematics and Computer Science 13 1 57–62.
IEEE Y. Nacaroğlu, “On Join Operation of Graphs by Obtained Monogenic Semigroups”, TJMCS, vol. 13, no. 1, pp. 57–62, 2021, doi: 10.47000/tjmcs.756323.
ISNAD Nacaroğlu, Yaşar. “On Join Operation of Graphs by Obtained Monogenic Semigroups”. Turkish Journal of Mathematics and Computer Science 13/1 (June 2021), 57-62. https://doi.org/10.47000/tjmcs.756323.
JAMA Nacaroğlu Y. On Join Operation of Graphs by Obtained Monogenic Semigroups. TJMCS. 2021;13:57–62.
MLA Nacaroğlu, Yaşar. “On Join Operation of Graphs by Obtained Monogenic Semigroups”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 1, 2021, pp. 57-62, doi:10.47000/tjmcs.756323.
Vancouver Nacaroğlu Y. On Join Operation of Graphs by Obtained Monogenic Semigroups. TJMCS. 2021;13(1):57-62.