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Banhatti-Sombor Index over a Graph of a Special Class of Semigroup

Year 2022, Volume: 10 Issue: 1, 40 - 43, 15.04.2022

Seda Oğuz Ünal

Abstract

Kulli introduced the first Banhatti-Sombor index in [18] which is outlined as

\begin{eqnarray*}
BSO_{1}(G)=\sum_{uv\in E(G)}\frac{1}{\sqrt{(d_{u})^{2}+(d_{v})^{2}}}.
\end{eqnarray*}

Our research will be calculated on an algebraic formation, utilising the chief principals of Banhatti-Sombor index of monogenic semigroup graphs which was first studied by [12].

Keywords

Monogenic semigroups Graphs Indices.

References

  • [1] Akgunes, N. and C¸ evik, A.S., A new bound of radius of irregularity index, Appl. Math. Comput. Vol:219, (2013), 5750-5753.
  • [2] Akgunes, N., Das, K. C. and C¸ evik, A. S., Topological indices on a graph of monogenic semigroups, Topics in Chemical Graph Theory, Vol:16, (2014), 3-20.
  • [3] Akgunes, N. and C¸ a˘gan, B., On the dot product of graphs over monogenic semigroups, Applied Mathematics and Computation, Vol:322, (2018), 1-5.
  • [4] Akgunes, N., A further note on the graph of monogenic semigroups, Konuralp Journal of Mathematics, Vol:6, No.1 (2018), 49-53.
  • [5] Akgunes, N. and Nacaroglu Y., On The Sigma Index of The Corona Products of Monogenic Semigroup Graphs, Journal of Universal Mathematics, Vol:2, No.1 (2019), 68-74.
  • [6] Akgunes¸, N., Nacaro˘glu Y. and Pak, S., Line Graphs of Monogenic Semigroup Graphs, Journal of Mathematics, Article ID 6630011, 4 pages, (2021), https://doi.org/10.1155/2021/6630011
  • [7] Alikhani, S. and Ghanbari, N., Sombor index of polymers, MATCH Commun. Math. Comput. Chem. Vol:86, (2021), 715-728.
  • [8] Amin, S., Rehman Virk, A. U., Rehman, M. A. and Shah, N. A., Analysis of dendrimer generation by Sombor indices, Hindawi Journal of Chemistry (2021), #9930645.
  • [9] Anderson, DD, Naseer, M, Beck’s coloring of a commutative ring, J. Algebra Vol:159, (1991), 500-514.
  • [10] Anderson, D.F. and Livingston, P., The Zero-divisor Graph of Commutative Ring, Journal of Algebra Vol:217, (1999), 434-447.
  • [11] Anderson, D.F. and Badawi, A., On the Zero-Divisor Graph of a Ring, Communications in Algebra Vol:36 No.8, (2008), 3073-3092.
  • [12] Beck, I., Coloring of Commutating Rings, J. Algebra, Neue Folge, Vol:116, (1988), 208-226.
  • [13] Cruz, R., Gutman, I. and Rada, J., Sombor index of chemical graphs, Appl. Math. Comput. Vol:399 (2021), #126018.
  • [14] Das, K. C., Akg¨unes¸ N., C¸ evik, A.S., On a graph of monogenic semigroup, J. Ineq. Appl., Vol:44, (2013), 1-13.
  • [15] Das, K. C., C¸ evik, A. S., Cang¨ul, I. N. and Shang, Y., On Sombor index, Symmetry, Vol:13, (2021), Art 140.
  • [16] DeMeyer, F.R. and DeMeyer, L., Zero-Divisor Graphs of Semigroups, J. Algebra, Vol:283, (2005), 190-198.
  • [17] DeMeyer, F.R., McKenzie, T. and Schneider, K., The Zero-Divisor Graph of a Commutative Semigroup, Semigroup Forum, Vol:65, (2002), 206-214.
  • [18] Gutman, I., Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. Vol:86, (2021), 11-16.
  • [19] Horoldagva, B. and Xu, C., On Sombor index of graphs, MATCH Commun. Math. Comput. Chem. Vol:86, (2021), 793-713.
  • [20] Kulli, V. R., On Banhatti-Sombor Indices, International Journal of Applied Chemistry Vol:8, No.1 (2021), 21-25.
  • [21] Liu, H., You, L. and Huang, Y., Ordering chemical graphs by Sombor indices and its applications, MATCH Commun. Math. Comput. Chem. Vol:87 (2022), In press.
  • [22] Milovanovic, I., Milovanovic, E. and Ali, A., M. Matejic, Some results on the Sombor indices of graphs, Contrib. Math. Vol:3 (2021), 59-67.
  • [23] Og˘uz U¨ nal, S. An application of Sombor index over a special class of semigroup graph, Journal of Mathematics (2021), https://doi.org/10.1155/2021/3273117
  • [24] O˘guz ¨ Unal, S. Nirmala index over a graph of a monogenic semigroup, Bulletin of IMVI (2022), https://doi.org/10.7251/BIMVI2201119¨U
  • [25] Rada, J., Rodr´ıguez, J. M. and Sigarreta, J. M., General properties on Sombor indices, Discrete Appl. Math. Vol:299 (2021), 87-97.
  • [26] Redˇzepovi´c, I., Chemical applicability of Sombor indices, J. Serb. Chem. Soc. Vol:86 (2021), 445-457.
  • [27] Todeschini, R. and Consonni, V., Molecular Descriptors for Chemoinformatics Wiley VCH. Weinheim (2009).

Year 2022, Volume: 10 Issue: 1, 40 - 43, 15.04.2022

Seda Oğuz Ünal

Abstract

References

  • [1] Akgunes, N. and C¸ evik, A.S., A new bound of radius of irregularity index, Appl. Math. Comput. Vol:219, (2013), 5750-5753.
  • [2] Akgunes, N., Das, K. C. and C¸ evik, A. S., Topological indices on a graph of monogenic semigroups, Topics in Chemical Graph Theory, Vol:16, (2014), 3-20.
  • [3] Akgunes, N. and C¸ a˘gan, B., On the dot product of graphs over monogenic semigroups, Applied Mathematics and Computation, Vol:322, (2018), 1-5.
  • [4] Akgunes, N., A further note on the graph of monogenic semigroups, Konuralp Journal of Mathematics, Vol:6, No.1 (2018), 49-53.
  • [5] Akgunes, N. and Nacaroglu Y., On The Sigma Index of The Corona Products of Monogenic Semigroup Graphs, Journal of Universal Mathematics, Vol:2, No.1 (2019), 68-74.
  • [6] Akgunes¸, N., Nacaro˘glu Y. and Pak, S., Line Graphs of Monogenic Semigroup Graphs, Journal of Mathematics, Article ID 6630011, 4 pages, (2021), https://doi.org/10.1155/2021/6630011
  • [7] Alikhani, S. and Ghanbari, N., Sombor index of polymers, MATCH Commun. Math. Comput. Chem. Vol:86, (2021), 715-728.
  • [8] Amin, S., Rehman Virk, A. U., Rehman, M. A. and Shah, N. A., Analysis of dendrimer generation by Sombor indices, Hindawi Journal of Chemistry (2021), #9930645.
  • [9] Anderson, DD, Naseer, M, Beck’s coloring of a commutative ring, J. Algebra Vol:159, (1991), 500-514.
  • [10] Anderson, D.F. and Livingston, P., The Zero-divisor Graph of Commutative Ring, Journal of Algebra Vol:217, (1999), 434-447.
  • [11] Anderson, D.F. and Badawi, A., On the Zero-Divisor Graph of a Ring, Communications in Algebra Vol:36 No.8, (2008), 3073-3092.
  • [12] Beck, I., Coloring of Commutating Rings, J. Algebra, Neue Folge, Vol:116, (1988), 208-226.
  • [13] Cruz, R., Gutman, I. and Rada, J., Sombor index of chemical graphs, Appl. Math. Comput. Vol:399 (2021), #126018.
  • [14] Das, K. C., Akg¨unes¸ N., C¸ evik, A.S., On a graph of monogenic semigroup, J. Ineq. Appl., Vol:44, (2013), 1-13.
  • [15] Das, K. C., C¸ evik, A. S., Cang¨ul, I. N. and Shang, Y., On Sombor index, Symmetry, Vol:13, (2021), Art 140.
  • [16] DeMeyer, F.R. and DeMeyer, L., Zero-Divisor Graphs of Semigroups, J. Algebra, Vol:283, (2005), 190-198.
  • [17] DeMeyer, F.R., McKenzie, T. and Schneider, K., The Zero-Divisor Graph of a Commutative Semigroup, Semigroup Forum, Vol:65, (2002), 206-214.
  • [18] Gutman, I., Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. Vol:86, (2021), 11-16.
  • [19] Horoldagva, B. and Xu, C., On Sombor index of graphs, MATCH Commun. Math. Comput. Chem. Vol:86, (2021), 793-713.
  • [20] Kulli, V. R., On Banhatti-Sombor Indices, International Journal of Applied Chemistry Vol:8, No.1 (2021), 21-25.
  • [21] Liu, H., You, L. and Huang, Y., Ordering chemical graphs by Sombor indices and its applications, MATCH Commun. Math. Comput. Chem. Vol:87 (2022), In press.
  • [22] Milovanovic, I., Milovanovic, E. and Ali, A., M. Matejic, Some results on the Sombor indices of graphs, Contrib. Math. Vol:3 (2021), 59-67.
  • [23] Og˘uz U¨ nal, S. An application of Sombor index over a special class of semigroup graph, Journal of Mathematics (2021), https://doi.org/10.1155/2021/3273117
  • [24] O˘guz ¨ Unal, S. Nirmala index over a graph of a monogenic semigroup, Bulletin of IMVI (2022), https://doi.org/10.7251/BIMVI2201119¨U
  • [25] Rada, J., Rodr´ıguez, J. M. and Sigarreta, J. M., General properties on Sombor indices, Discrete Appl. Math. Vol:299 (2021), 87-97.
  • [26] Redˇzepovi´c, I., Chemical applicability of Sombor indices, J. Serb. Chem. Soc. Vol:86 (2021), 445-457.
  • [27] Todeschini, R. and Consonni, V., Molecular Descriptors for Chemoinformatics Wiley VCH. Weinheim (2009).
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Seda Oğuz Ünal

Publication Date April 15, 2022
Submission Date February 15, 2022
Acceptance Date April 6, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

APA Oğuz Ünal, S. (2022). Banhatti-Sombor Index over a Graph of a Special Class of Semigroup. Konuralp Journal of Mathematics, 10(1), 40-43.
AMA Oğuz Ünal S. Banhatti-Sombor Index over a Graph of a Special Class of Semigroup. Konuralp J. Math. April 2022;10(1):40-43.
Chicago Oğuz Ünal, Seda. “Banhatti-Sombor Index over a Graph of a Special Class of Semigroup”. Konuralp Journal of Mathematics 10, no. 1 (April 2022): 40-43.
EndNote Oğuz Ünal S (April 1, 2022) Banhatti-Sombor Index over a Graph of a Special Class of Semigroup. Konuralp Journal of Mathematics 10 1 40–43.
IEEE S. Oğuz Ünal, “Banhatti-Sombor Index over a Graph of a Special Class of Semigroup”, Konuralp J. Math., vol. 10, no. 1, pp. 40–43, 2022.
ISNAD Oğuz Ünal, Seda. “Banhatti-Sombor Index over a Graph of a Special Class of Semigroup”. Konuralp Journal of Mathematics 10/1 (April 2022), 40-43.
JAMA Oğuz Ünal S. Banhatti-Sombor Index over a Graph of a Special Class of Semigroup. Konuralp J. Math. 2022;10:40–43.
MLA Oğuz Ünal, Seda. “Banhatti-Sombor Index over a Graph of a Special Class of Semigroup”. Konuralp Journal of Mathematics, vol. 10, no. 1, 2022, pp. 40-43.
Vancouver Oğuz Ünal S. Banhatti-Sombor Index over a Graph of a Special Class of Semigroup. Konuralp J. Math. 2022;10(1):40-3.
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