We find
some upper bounds for the product of the SDD and ISDD indices, and discuss the
graphs were the equalities are attained. Our bounds allow us to find new upper
bounds for the ISDD index, using previously known lower bounds for the SDD
index.
References
[1]
Palacios, J.L. (2019) New Upper Bounds for the Symmetric Division Deg Index of Graphs. Discrete Mathematics Letters, 2, 52-56.
[2]
Wilson, R.J. (1972) Introduction to Graph Theory. Oliver & Boyd, Edinburgh.
[3]
Vukičević, D. and Gašperov, M. (2010) Bond Additive Modeling 1. Adriatic Indices. Croatica Chemica Acta, 83, 243-260.
[4]
Das, K.C., Matejić, M., Milovanović, E. and MIlovanović, I. (2019) Bounds for Symmetric Division Deg Index of Graphs. Filomat, 33, 683-698. https://doi.org/10.2298/FIL1903683D
[5]
Furtula, B., Das, K.C. and Gutman, I. (2018) Comparative Analysis of Symmetric Division Deg Index as Potentially Useful Molecular Descriptor. International Journal of Quantum Chemistry, 118, e25659. https://doi.org/10.1002/qua.25659
[6]
Gupta, C.K., Lokesha, V., Shwetha, B.S. and Ranjini, P.S. (2016) On the Symmetric Division Deg Index of Graph. Southeast Asian Bulletin of Mathematics, 40, 59-80.
[7]
Bianchi, M., Cornaro, A., Palacios, J.L. and Torriero, A. (2016) Upper and Lower Bounds for the Mixed Degree-Kirchhoff Index. Filomat, 30, 2351-2358. https://doi.org/10.2298/FIL1609351B
[8]
Ghorbani, M., Zangi, S. and Amraei, N. (2021) New Results on Symmetric Division Deg Index. Journal of Computational and Applied Mathematics, 65, 161-176. https://doi.org/10.1007/s12190-020-01386-9
[9]
Albalahi, A.M. and Ali, A. (2022) On the Inverse Symmetric Division Deg Index of Unicyclic Graphs. Computation, 10, 181. https://doi.org/10.3390/computation10100181
[10]
Raza, Z., Saha, L. and Das, K.C. (2023) On Inverse Symmetric Division Deg Index of Graphs. RAIRO, 57, 3223-3236. https://doi.org/10.1051/ro/2023181
[11]
Palacios, J.L. (2024) More on Topological Indices and Their Reciprocals. MATCH Communications in Mathematical and in Computer Chemistry. 92, 55-63. https://doi.org/10.46793/match.92-1.055P
[12]
Schweitzer, P. (1914) An Inequality about the Arithmetic Mean. Matematikai és Physikai Lapok, 23, 257-261.
[13]
Lupaş, A. (1972) A Remark on the Schweitzer and Kantorovich Inequalities. Publikacije Elektrotehničkog Fakulteta Univerziteta u Beogradu, Serija: Matematica i fizika, 383, 13-14.
[14]
Gutman, I. and Trinajstić, N. (1972) Graph Theory and Molecular Orbitals. Total π-Electron Energy of Alternant Hydrocarbons. Chemical Physics Letters, 17, 535-538. https://doi.org/10.1016/0009-2614(72)85099-1
[15]
Gutman, I., Ruscić, B., Trinajstić, N. and Wilcox, C.F. (1975) Graph Theory and Molecular Orbitals. XII. Acyclic Ployenes. The Journal of Chemical Physics, 62, 3399-3405. https://doi.org/10.1063/1.430994
