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).