On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs

Yıl 2022, Cilt: 4 Sayı: 2, 12 - 20, 31.12.2022

Seda Oğuz Ünal

https://doi.org/10.54286/ikjm.1160312

Öz

Albertson and the reduced Sombor indices are vertex-degree-based graph invariants that given in [5] and [18], defined as

Alb(G)=\sum_{uv\in E(G)}\left|d_{u}-d_{v}\right|, SO_{red}(G)=\sum_{uv\in E(G)}\sqrt{(d_{u}-1)^{2}+(d_{v}-1)^{2}},

respectively.

In this work we show that a calculation of Albertson and reduced Sombor index which are vertex-degree-based topological indices, over monogenic semigroup graphs.

Anahtar Kelimeler

Monogenic semigroups, Graphs, Indices

Kaynakça

• Akgüneş, N., Ç evik, A.S., A new bound of radius of irregularity index, Appl. Math. Comput. 219 (2013), 5750-5753.
• Akgüneş, N., Das, K. C., Ç evik, A. S., Topological indices on a graph of monogenic semigroups in Topics in Chemical Graph Theory, Mathematical Chemistry Monographs, I. Gutman, Ed., University of Kragujevac and Faculty of Science Kragujevac, Kragujevac, Serbia, (2014).
• Akgüneş, N., Çağan, B., On the dot product of graphs over monogenic semigroups, Applied Mathematics and Computation, 322, (2018) 1-5.
• Akgüneş, N., A further note on the graph of monogenic semigroups, Konuralp Journal of Mathematics, 6(1), (2018) 49-53.
• Albertson, M. O., The irregularity of a graph, Ars Combinatoria, 46, (1997) 219-225.
• Alikhani, S., Ghanbari, N., Sombor index of polymers, MATCH Commun. Math. Comput. Chem. 86 (2021) 715-728.
• Amin, S., Rehman Virk, A. U., Rehman, M. A., Shah, N. A., Analysis of dendrimer generation by Sombor indices, Hindawi Journal of Chemistry (2021) #9930645.
• Anderson, DD, Naseer, M, Beck’s coloring of a commutative ring, J. Algebra 159, (1991), 500-514.
• Anderson, D.F., Livingston, P., The Zero-divisor Graph of Commutative Ring, Journal of Algebra 217, (1999), 434-447.
• Anderson, D.F., Badawi, A., On the Zero-Divisor Graph of a Ring Communications in Algebra 36(8), (2008), 3073-3092.
• Beck, I., Coloring of Commutating Rings, J. Algebra, Neue Folge, Vol. 116, (1988), 208-226.
• Cruz, R., Gutman, I., Rada, J., Sombor index of chemical graphs, Appl. Math. Comput. 399 (2021) #126018.
• Das, K. C., Akgüneş N., Çevik, A.S., On a graph of monogenic semigroup, J. Ineq. Appl., 44, (2013).
• Das, K. C., Çevik, A. S., Cangül, I. N., Shang, Y., On Sombor index, Symmetry, 13, (2021), Art 140.
• DeMeyer, F.R., DeMeyer, L., Zero-Divisor Graphs of Semigroups, J. Algebra, 283, (2005), 190-198.
• DeMeyer, F.R., McKenzie, T., Schneider, K., The Zero-Divisor Graph of a Commutative Semigroup, Semigroup Forum, 65, (2002), 206-214.
• Devillers, J., Balaban A. T.(Eds), Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, (1999).
• Gutman, I., Geometric approach to degree-based topological indices: Sombor indices , MATCH Commun. Math. Comput. Chem. 86 (2021), 11-16.
• Gutman, I., Spectrum and energy of the Sombor matrix, Military Technical Courier 69 (2021), 551-561.
• Gutman, I., Some basic properties of Sombor indices, Open J. Discr. Appl. Math. 4 (2021) 1–3.
• Horoldagva, B., Xu, C., On Sombor index of graphs, MATCH Commun. Math. Comput. Chem. 86 (2021) 793-713.
• Liu, H., You, L., Huang, Y., Ordering chemical graphs by Sombor indices and its applications, MATCH Commun. Math. Comput. Chem. 87 (2022), 5–22.
• Liu, H.; Gutman, I.; You, L.; Huang, Y. Sombor index: review of extremal results and bounds. J. Math. Chem. 2022, 66, 771–798.
• Milovanovic, I., Milovanovic, E., Ali, A., M. Matejic, Some results on the Sombor indices of graphs, Contrib. Math. 3 (2021) 59-67.
• Oğuz Ünal, S. An application of Sombor index over a special class of semigroup graph. J. Math. 2021, 3273117.
• Oğuz Ünal, S. Sombor index over the tensor and Cartesian product of monogenic semigroup graphs. Symmetry, 14(5), 2021, #1071.
• Rada, J., Rodr´ıguez, J. M., Sigarreta, J. M., General properties on Sombor indices, Discrete Appl. Math. 299 (2021) 87-97.
• Redzepovic, I., Chemical applicability of Sombor indices, J. Serb. Chem. Soc. 86 (2021) 445-457.
• Reti, T., Doslic, T., Ali, A., On the Sombor index of graphs, Contrib. Math. 3 (2021) 11-18.
• Doslic, T., Reti, T., Ali, A., On the structure of graphs with integer Sombor indices, Discrete Math. Lett. 7(2021) 1-4.
• Shang, Y. Sombor index and degree-related properties of simplicial networks. Appl. Math. Comput. 2022, 419, 126881.
• Todeschini, R., Consonni, V., Molecular Descriptors for Chemoinformatics Wiley VCH. Weinheim (2009).
• West, D.B. An Introduction to Graph Theory; Prentice-Hall: Upper Saddle River, NJ, USA, 1996.