On relations between inverse sum indeg index and multiplicative sum Zagreb index
Authors: Matejić M.M., Milovanović E.I., Milovanović I.Ž.
Keywords: Vertex degree; inverse sum indeg index; multiplicative sum Zagreb index
Abstract:
In this paper we derive some lower and upper bounds for the inverse sum indeg index, ISI = Σi~j didj di+dj, in terms of graph invariants F = Σni =1 d3i and Π* 1 = Πi~j(di+dj).
References:
[1] Biernacki, M., Pidek, H., Ryll-Nardzewski, C. (1950) Sur une inegalite entre des integrales definies. Annales Univ. Mariae Curie-Sklodowska A, 4, 1-4
[2] Borovićanin, B., Das, K.C., Furtula, B., Gutman, I. (2017) Bounds for Zagreb indices. MATCH Commun. Math. Comput. Chem, 78, 17-100
[3] Borovićanin, B., Das, K.C., Furtula, B., Gutman, I. (2017) Zagreb indices: Bounds and extremal graphs. u: Gutman I., Furtula B.Das K.C.Milovanović E.Milovanović I. [ur.] Bounds in Chemical Graph Theory – Basics, Kragujevac: Univ. Kragujevac, Mathematical Chemistry Monographs, MCM 19, pp. 67-153
[4] Eliasi, M., Iranmanesh, A., Gutman, I. (2012) Multiplicative versions of first Zagreb index. Communications in Mathematical and in Computer Chemistry / MATCH, vol. 68, br. 1, str. 217-230
[5] Falahati-Nezhad, F., Azari, M., Došlić, T. (2017) Sharp bounds on the inverse sum indeg index. Discrete Applied Mathematics, 217: 185-195
[6] Furtula, B., Gutman, I. (2015) A forgotten topological index. Journal of Mathematical Chemistry, 53(4): 1184-1190
[7] Gutman, I., Trinajstić, N. (1972) Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons. Chemical Physics Letters, 17(4): 535-538
[8] Gutman, I. (2011) Multiplicative Zagreb indices of trees. Bull. Int. Math. Virt. Inst., 1, 13-19
[9] Gutman, I., das Kinkar, Ch. (2004) The first Zagreb index 30 years after. Communications in mathematical and in computer chemistry / MATCH, br. 50, str. 83-92
[10] Kober, H. (1958) On the arithmetic and geometric means and on Hölder’s inequality. Proceedings of the American Mathematical Society, 9(3): 452-452
[11] Milovanović, I.Ž., Milovanović, E.I., Gutman, I., Furtula, B. (2017) Some inequalities for the forgotten topological index. Int. J. Appl. Graph Theory, 1 (1): 1-15
[12] Nikolić, S., Kovačević, G., Miličević, A., Trinajstić, N. (2003) The Zagreb indices 30 years after. Croat. Chem. Acta, 113-124; 76
[13] Sedlar, J., Stevanović, D., Vasilyev, A. (2015) On the inverse sum indeg index. Discrete Applied Mathematics, 184: 202-212
[14] Szökefalvi, N.J. (1918) Über algebraische Gleichungen mit lauter reellen Wurzeln. Jahresbericht der deutschen mathematiker-Vereingung, 27, 37-43
[15] Todeschini, R., Consonni, V. (2010) New local vertex invariants and molecular descriptors based on functions of the vertex degrees. MATCH Commun. Math. Comput. Chem., 64 (2): 359-372
[16] Vukičević, D., Gašperov, M. (2010) Bond additive modeling 1: Adriatic indices. Croat. Chem. Acta, 83, 243-260
[17] Vukičević, D. (2010) Bond additive modeling 2: Mathematical properties of max-min rodeg index. Croat. Chem. Acta, 83(3): 261-273
[18] Zhou, B., Gutman, I., Aleksić, T. (2008) A note on the Laplacian energy of graphs. MATCH Commun. Math. Comput. Chem, 60(2): 441-446