First irregularity Sombor index of trees with fixed maximum degree

References

• Akhter, S., & Farooq, R. (2020). Eccentric adjacency index of graphs with a given number of cut edges. Bulletin of the Malaysian Mathematical Sciences Society, 43(3), 2509–2522. https://doi.org/10.1007/s40840-019-00820-x
   Web of Science ®Google Scholar
• Ali, A., Chartrand, G., & Zhang, P. (2021). Irregularity in graphs. Springer.
   Google Scholar
• Ashrafi, A., Došlić, T., & Hamzeh, A. (2010). The Zagreb coindices of graph operations. Discrete Applied Mathematics, 158(15), 1571–1578. https://doi.org/10.1016/j.dam.2010.05.017
   Web of Science ®Google Scholar
• Azari, M., Dehgardi, N., & Došlić, T. (2023). Lower bounds on the irregularity of trees and unicyclic graphs. Discrete Applied Mathematics, 324, 136–144. https://doi.org/10.1016/j.dam.2022.09.022
   Web of Science ®Google Scholar
• Cruz, R., & Rada, J. (2021). Extremal values of the Sombor index in unicyclic and bicyclic graphs. Journal of Mathematical Chemistry, 59(4), 1098–1116. https://doi.org/10.1007/s10910-021-01232-8
   Web of Science ®Google Scholar
• Das, K. C., Cevik, A. S., Cangul, I. N., & Shang, Y. (2021). On Sombor index. Symmetry, 13(1), 140. https://doi.org/10.3390/sym13010140
   Google Scholar
• Das, K. C., & Shang, Y. (2021). Some extremal graphs with respect to Sombor index. Mathematics, 9(11), 1202. https://doi.org/10.3390/math9111202
   Web of Science ®Google Scholar
• Dehgardi, N., & Liu, J.-B. (2021). Lanzhou index of trees with fixed maximum degree. MATCH Communications in Mathematical and in Computer Chemistry, 86(1), 3–10.
   Web of Science ®Google Scholar
• Došlić, T. (2008). Vertex-weighted Wiener polynomials for composite graphs. Ars Mathematica Contemporanea, 1(1), 66–80. https://doi.org/10.26493/1855-3974.15.895
   Web of Science ®Google Scholar
• Došlić, T., Réti, T., & Ali, A. (2021). On the structure of graphs with integer Sombor indices. Discrete Mathematics Letters, 7, 1–4. https://doi.org/10.47443/dml.2021.0012
   Google Scholar
• Farooq, R., Akhter, S., & Rada, J. (2022). Total eccentricity index of trees with fixed pendent vertices and trees with fixed diameter. Japan Journal of Industrial and Applied Mathematics, 39(1), 443–465. https://doi.org/10.1007/s13160-021-00494-8
   Web of Science ®Google Scholar
• Farooq, R., Malik, M. A., & Rada, J. (2023). Extremal graphs with respect to the total-eccentricity index. Asian-European Journal of Mathematics, 16(8), 2350138. https://doi.org/10.1142/S1793557123501383
   Google Scholar
• Gutman, I. (2011). Multiplicative Zagreb indices of trees. Bulletin of International Mathematical Virtual Institute, 1, 13–19.
   Google Scholar
• Gutman, I. (2021). Geometric approach to degree-based topological indices: Sombor indices. MATCH Communications in Mathematical and in Computer Chemistry, 86(1), 11–16.
   Web of Science ®Google Scholar
• Gutman, I., Furtula, B., Vukičević, K., & Popivoda, G. (2015). On Zagreb indices and coindices. MATCH Communications in Mathematical and in Computer Chemistry, 74(1), 5–16.
   Web of Science ®Google Scholar
• Gutman, I., Redžepović, I., & Kulli, R. K. (2022). KG-Sombor index of Kragujevac trees. Open Journal of Discrete Applied Mathematics, 5(1), 25–28. https://doi.org/10.30538/psrp-odam2022.0067
   Google Scholar
• Kosari, S., Dehgardi, N., & Khan, A. (2023). Lower bound on the KG-Sombor index, commun. Communications in Combinatorics and Optimization, 8(4), 751–757. https://doi.org/10.22049/CCO.2023.28666.1662
   Web of Science ®Google Scholar
• Kulli, V. R. (2021). New irregularity Sombor indices and new Adriatic (a, b)-KA indices of certain chemical drugs. International Journal of Mathematics Trends and Technology, 67(9), 105–113. https://doi.org/10.14445/22315373/IJMTT-V67I9P512
   Google Scholar
• Kulli, V. R., & Gutman, I. (2021). Computation of Sombor indices of certain networks. International Journal of Applied Chemistry, 8(1), 1–5. https://doi.org/10.14445/23939133/IJAC-V8I1P101
   Google Scholar
• Liu, H., You, L., Tang, Z., & Liu, J. B. (2021). On the reduced Sombor index and its applications. MATCH Communications in Mathematical and in Computer Chemistry, 86(3), 729–753.
   Web of Science ®Google Scholar
• Ma, Y., Cao, S., Shi, Y., Dehmer, M., & Xia, C. (2019). Nordhaus-Gaddum type results for graph irregularities. Applied Mathematics and Computation, 343, 268–272. https://doi.org/10.1016/j.amc.2018.09.057
   Web of Science ®Google Scholar
• Ramane, H. S., Gutman, I., Bhajantri, K., & Kitturmath, D. V. (2023). Sombor index of some graph transformations, commun. Communications in Combinatorics and Optimization, 8(1), 193–205. https://doi.org/10.22049/CCO.2021.27484.1272
   Google Scholar
• Rasi, R., Sheikholeslami, S. M., & Behmaram, A. (2017). An upper bound on the first Zagreb index and coindex in trees. The Iranian Journal of Mathematical Chemistry (IJMC), 8(1), 71–82. https://doi.org/10.22052/ijmc.2017.42995
   Google Scholar
• Shang, Y. (2022). Sombor index and degree-related properties of simplicial networks. Applied Mathematics and Computation, 419, 126881. https://doi.org/10.1016/j.amc.2021.126881
   Web of Science ®Google Scholar
• Vukičević, D., Li, Q., Sedlar, J., & Došlić, T. (2018). Lanzhou Index. MATCH Communications in Mathematical and in Computer Chemistry, 80(3), 863–876.
   Web of Science ®Google Scholar
• Xu, K., & Hua, H. (2012). A unified approach to extremal multiplicative Zagreb indices for trees, unicyclic and bicyclic graphs. MATCH Communications in Mathematical and in Computer Chemistry, 68(1), 241–256.
   Web of Science ®Google Scholar
• Yousaf, S., Bhatti, A. A., & Ali, A. (2020). A note on the modified Albertson index. Discrete Dynamics in Nature & Society, 2020, 1–4. https://doi.org/10.1155/2020/3976274
   Google Scholar
• Zhou, B., & Luo, W. (2008). On irregularity of graphs. Ars Combinatoria, 88, 55–64.
   Web of Science ®Google Scholar