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Kimyasal Grafların Euler Sombor İndeksi

Year 2025, Volume: 6 Issue: 1, 146 - 160, 29.05.2025

Gül Özkan Kızılırmak , İvan Gutman

https://doi.org/10.63716/guffd.1605825

Abstract

G basit bir graf olsun. G'nin Euler Sombor indeksi
EU(G)=∑_uv▒‍ √(d_u^2+d_v^2+(d_u d_v ) ),
şeklinde tanımlıdır. Burada, d_u, u noktasının derecesini belirtir ve toplam, G'nin kenalar kümesi üzerinde ilerler. Bu makalede amacımız, eşit sayıda nokta sayısına sahip bağlantılı kimyasal graflar kümesi ve kimyasal ağaçlar kümesi üzerinde EU'nun ekstrem değer problemini çözmektir.

Keywords

Euler Sombor indeks Kimyasal Graf Nokta derecesine bağlı topolojik indeks

References

  • Gutman, I. (2021). Geometric approach to degree-based topological indices: Sombor indices. MATCH Communications in Mathematical and in Computer Chemistry, 86, 11–16.
  • Das, K.C., Cevik, A.S., Cangul, I.N., Shang, Y. (2021). On Sombor index. Symmetry, 13, 140.
  • Cruz, R., Gutman, I. and Rada, J. (2021). Sombor index of chemical graphs. Applied Mathematics and Computation, 399, 126018.
  • Liu, H., Chen, H., Xiao, Q., Fang, X. and Tang, Z. (2021). More on Sombor indices of chemical graphs and their applications to the boiling point of benzenoid hydrocarbons. Internatioal Journal of Quantum Chemistry, 121(17), e26689.
  • Redzepovic, I. (2021). Chemical applicability of Sombor indices. Journal of Serbian Chemical Society, 86, 445-457.
  • Méndez-Bermúdez, J.A., Aguilar-Sánchez, R., Molina, E.D. and Rodríguez, J.M. (2022). Mean Sombor index. Discrete Mathematics Letters, 9, 18–25.
  • Kulli, V.R. (2023). Delta Banhatti-Sombor indices of certain networks. International Journal of Mathematics and Computer Research, 11, 3875–3881.
  • Kulli, V.R. (2023). Modified domination Sombor index and its exponential of a graph. International Journal of Mathematics and Computer Research, 11, 3639–3644.
  • Du, Z., You, L., Liu, H. and Huang, Y. (2023). The Sombor index and coindex of two-trees. AIMS Mathematics, 8, 18982–18994.
  • Du, Z., You, L., Liu, H. and Huang, Y. (2024). The Sombor index and coindex of chemical graphs. Polycyclic Aromatic Compounds, 44, 2942–2965.
  • X. Chen, B. Wu and Z. Li. (2025). Sombor index and elliptic Sombor index of benzenoid systems. MATCH Communications in Mathematical and in Computer Chemistry, 94, 263-285.
  • Gutman, I., Furtula, B. and Oz, M.S. (2024). Geometric approach to vertex degree based topological indices Elliptic Sombor index theory and application. International Journal of Quantum Chemistry, 124(2), e27346.
  • Özkan Kızılırmak, G. (2024). Graf İşlemlerinin Eliptik Sombor tamamlayıcı indeksi için sınırlar. Gazi Üniversitesi Fen Fakültesi Dergisi, 5(1), 1–10. Tang, Z., Li, Y.and Deng, H. (2024). The Euler Sombor index of a graph, International Journal of Quantum Chemistry, 124(9), e27387.
  • Hu, Y., Fang, J., Liu, Y. and Lin, Z. (2024). Bounds on the Euler Sombor index of maximal outerplanar graphs, Electronic Journal of Mathematics, 8, 39–47.
  • Gutman, I. (2024). Relating Sombor and Euler indices. Military Technical Courier, 72(1), 1–12.
  • Hayat, S., Arshad, M., Khan, A. (2023). Graphs with given connectivity and their minimum Sombor index having applications to QSPR studies of monocarboxylic acids. Heliyon, 10, e23392.
  • Shashidhara, A.A., Ahmed, H., Nandappa, S. and Cancan, M. (2023). Domination version: Sombor index of graphs and its significance in predicting physicochemical properties of butane derivatives. Eurasian Chemistry Communications, 5, 91–102.
  • Cruz R., Gutman I., Rada J. (2021). Sombor index of chemical graphs. Applied Mathematics and Computation, 399, 126018.
  • Afzal, H.U., Fatima, T. (2019). On Topological Indices of OT [m,n] Octagonal Tillings and 〖TiO〗_2 Nanotubes. Acta Chimica Slovenica, 66, 435–442.
  • Aqib, M., Ali Malik, M., Usman Afzal, H., Fatima, T. and Ali, Y. (2023). On topological indices of some chemical graphs. Molecular Physics, e2276386.
  • Baig, A.Q., Imran, M., Ali, H. (2015). On topological indices of poly oxide, poly silicate, DOX, and DSL networks. Canadian Journal of Chemistry, 730–739.

Year 2025, Volume: 6 Issue: 1, 146 - 160, 29.05.2025

Gül Özkan Kızılırmak , İvan Gutman

https://doi.org/10.63716/guffd.1605825

Abstract

References

  • Gutman, I. (2021). Geometric approach to degree-based topological indices: Sombor indices. MATCH Communications in Mathematical and in Computer Chemistry, 86, 11–16.
  • Das, K.C., Cevik, A.S., Cangul, I.N., Shang, Y. (2021). On Sombor index. Symmetry, 13, 140.
  • Cruz, R., Gutman, I. and Rada, J. (2021). Sombor index of chemical graphs. Applied Mathematics and Computation, 399, 126018.
  • Liu, H., Chen, H., Xiao, Q., Fang, X. and Tang, Z. (2021). More on Sombor indices of chemical graphs and their applications to the boiling point of benzenoid hydrocarbons. Internatioal Journal of Quantum Chemistry, 121(17), e26689.
  • Redzepovic, I. (2021). Chemical applicability of Sombor indices. Journal of Serbian Chemical Society, 86, 445-457.
  • Méndez-Bermúdez, J.A., Aguilar-Sánchez, R., Molina, E.D. and Rodríguez, J.M. (2022). Mean Sombor index. Discrete Mathematics Letters, 9, 18–25.
  • Kulli, V.R. (2023). Delta Banhatti-Sombor indices of certain networks. International Journal of Mathematics and Computer Research, 11, 3875–3881.
  • Kulli, V.R. (2023). Modified domination Sombor index and its exponential of a graph. International Journal of Mathematics and Computer Research, 11, 3639–3644.
  • Du, Z., You, L., Liu, H. and Huang, Y. (2023). The Sombor index and coindex of two-trees. AIMS Mathematics, 8, 18982–18994.
  • Du, Z., You, L., Liu, H. and Huang, Y. (2024). The Sombor index and coindex of chemical graphs. Polycyclic Aromatic Compounds, 44, 2942–2965.
  • X. Chen, B. Wu and Z. Li. (2025). Sombor index and elliptic Sombor index of benzenoid systems. MATCH Communications in Mathematical and in Computer Chemistry, 94, 263-285.
  • Gutman, I., Furtula, B. and Oz, M.S. (2024). Geometric approach to vertex degree based topological indices Elliptic Sombor index theory and application. International Journal of Quantum Chemistry, 124(2), e27346.
  • Özkan Kızılırmak, G. (2024). Graf İşlemlerinin Eliptik Sombor tamamlayıcı indeksi için sınırlar. Gazi Üniversitesi Fen Fakültesi Dergisi, 5(1), 1–10. Tang, Z., Li, Y.and Deng, H. (2024). The Euler Sombor index of a graph, International Journal of Quantum Chemistry, 124(9), e27387.
  • Hu, Y., Fang, J., Liu, Y. and Lin, Z. (2024). Bounds on the Euler Sombor index of maximal outerplanar graphs, Electronic Journal of Mathematics, 8, 39–47.
  • Gutman, I. (2024). Relating Sombor and Euler indices. Military Technical Courier, 72(1), 1–12.
  • Hayat, S., Arshad, M., Khan, A. (2023). Graphs with given connectivity and their minimum Sombor index having applications to QSPR studies of monocarboxylic acids. Heliyon, 10, e23392.
  • Shashidhara, A.A., Ahmed, H., Nandappa, S. and Cancan, M. (2023). Domination version: Sombor index of graphs and its significance in predicting physicochemical properties of butane derivatives. Eurasian Chemistry Communications, 5, 91–102.
  • Cruz R., Gutman I., Rada J. (2021). Sombor index of chemical graphs. Applied Mathematics and Computation, 399, 126018.
  • Afzal, H.U., Fatima, T. (2019). On Topological Indices of OT [m,n] Octagonal Tillings and 〖TiO〗_2 Nanotubes. Acta Chimica Slovenica, 66, 435–442.
  • Aqib, M., Ali Malik, M., Usman Afzal, H., Fatima, T. and Ali, Y. (2023). On topological indices of some chemical graphs. Molecular Physics, e2276386.
  • Baig, A.Q., Imran, M., Ali, H. (2015). On topological indices of poly oxide, poly silicate, DOX, and DSL networks. Canadian Journal of Chemistry, 730–739.
There are 21 citations in total.

Details

Primary Language Turkish
Subjects Algebra and Number Theory
Journal Section Araştırma Makaleleri
Authors

Gül Özkan Kızılırmak 0000-0003-3263-8685

İvan Gutman 0000-0001-9681-1550

Publication Date May 29, 2025
Submission Date December 23, 2024
Acceptance Date May 5, 2025
Published in Issue Year 2025 Volume: 6 Issue: 1

Cite

APA Özkan Kızılırmak, G., & Gutman, İ. (2025). Kimyasal Grafların Euler Sombor İndeksi. Gazi Üniversitesi Fen Fakültesi Dergisi, 6(1), 146-160. https://doi.org/10.63716/guffd.1605825
AMA Özkan Kızılırmak G, Gutman İ. Kimyasal Grafların Euler Sombor İndeksi. GÜFFD. May 2025;6(1):146-160. doi:10.63716/guffd.1605825
Chicago Özkan Kızılırmak, Gül, and İvan Gutman. “Kimyasal Grafların Euler Sombor İndeksi”. Gazi Üniversitesi Fen Fakültesi Dergisi 6, no. 1 (May 2025): 146-60. https://doi.org/10.63716/guffd.1605825.
EndNote Özkan Kızılırmak G, Gutman İ (May 1, 2025) Kimyasal Grafların Euler Sombor İndeksi. Gazi Üniversitesi Fen Fakültesi Dergisi 6 1 146–160.
IEEE G. Özkan Kızılırmak and İ. Gutman, “Kimyasal Grafların Euler Sombor İndeksi”, GÜFFD, vol. 6, no. 1, pp. 146–160, 2025, doi: 10.63716/guffd.1605825.
ISNAD Özkan Kızılırmak, Gül - Gutman, İvan. “Kimyasal Grafların Euler Sombor İndeksi”. Gazi Üniversitesi Fen Fakültesi Dergisi 6/1 (May 2025), 146-160. https://doi.org/10.63716/guffd.1605825.
JAMA Özkan Kızılırmak G, Gutman İ. Kimyasal Grafların Euler Sombor İndeksi. GÜFFD. 2025;6:146–160.
MLA Özkan Kızılırmak, Gül and İvan Gutman. “Kimyasal Grafların Euler Sombor İndeksi”. Gazi Üniversitesi Fen Fakültesi Dergisi, vol. 6, no. 1, 2025, pp. 146-60, doi:10.63716/guffd.1605825.
Vancouver Özkan Kızılırmak G, Gutman İ. Kimyasal Grafların Euler Sombor İndeksi. GÜFFD. 2025;6(1):146-60.