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Year 2022, Volume: 4 Issue: 2, 12 - 20, 31.12.2022

Seda Oğuz Ünal

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

Abstract

References

  • 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.

On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs

Year 2022, Volume: 4 Issue: 2, 12 - 20, 31.12.2022

Seda Oğuz Ünal

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

Abstract

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.

Keywords

Monogenic semigroups Graphs Indices

References

  • 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.
There are 33 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Seda Oğuz Ünal

Early Pub Date December 31, 2022
Publication Date December 31, 2022
Acceptance Date October 13, 2022
Published in Issue Year 2022 Volume: 4 Issue: 2

Cite

APA Oğuz Ünal, S. (2022). On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs. Ikonion Journal of Mathematics, 4(2), 12-20. https://doi.org/10.54286/ikjm.1160312
AMA Oğuz Ünal S. On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs. ikjm. December 2022;4(2):12-20. doi:10.54286/ikjm.1160312
Chicago Oğuz Ünal, Seda. “On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs”. Ikonion Journal of Mathematics 4, no. 2 (December 2022): 12-20. https://doi.org/10.54286/ikjm.1160312.
EndNote Oğuz Ünal S (December 1, 2022) On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs. Ikonion Journal of Mathematics 4 2 12–20.
IEEE S. Oğuz Ünal, “On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs”, ikjm, vol. 4, no. 2, pp. 12–20, 2022, doi: 10.54286/ikjm.1160312.
ISNAD Oğuz Ünal, Seda. “On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs”. Ikonion Journal of Mathematics 4/2 (December 2022), 12-20. https://doi.org/10.54286/ikjm.1160312.
JAMA Oğuz Ünal S. On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs. ikjm. 2022;4:12–20.
MLA Oğuz Ünal, Seda. “On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs”. Ikonion Journal of Mathematics, vol. 4, no. 2, 2022, pp. 12-20, doi:10.54286/ikjm.1160312.
Vancouver Oğuz Ünal S. On Vertex-Degree-Based Indices of Monogenic Semigroup Graphs. ikjm. 2022;4(2):12-20.
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