some results on the forgotten index
Subject Areas : Statistics
Farzaneh
Falahati Nejad
1
(Assistant Professor, Department of Mathematics, Islamic Azad University, Safadasht Branch, Tehran, Iran)
Keywords: درجه راس, شاخص فراموش شده, کران, پایایی گراف,
Abstract :
Let G be a simple connected finite graph. A graph invariant (also known as topological index or molecular descriptor) of graph G is a real number with the property that for every graph H isomorphic to graph G, Top(H) = Top(G). The sum of cubes of vertex degrees of graph G was revived by Furtula and Gutman under the name of forgotten topological index. The Forgotten index F(G) of a simple graph G can also be expressed asF(G)=∑_(uv∈E(G))▒(〖〖〖d_u〗^2+d〗_v〗^2 ) whered_u denotes the degree of the vertex u of G. In this paper, we compare the F-index with some graph parameters such as order, size, radius, minimal vertex degree and maximal vertex degree and some well-known molecular descriptors consisting of first Zagreb index and second Zagreb index, first modified Zagreb index and second modified Zagreb index, Harmonic index, Eccentric connectivity index, hyper-Zagreb index, Geometric-Arithmetic index and inverse sum indeg index.
[1] M. Azari, Sharp lower bounds on the Narumi-Katayama index of graph operations, Appl. Math. Comput., 239C (2014) 409-421.
[2] M. Azari and A. Iranmanesh, Some inequalities for the multiplicative sum Zagreb index of graph operations, J. Math. Inequal., 9 (3) (2015), 727-738.
[3] K. C. Das, I. Gutman and B. Furtula, Survey on geometric–arithmetic indices of graphs, MATCH Commun. Math. Comput. Chem., 65(2011) 595-644.
[4] J. B. Diaz and F. T. Metcalf, Stronger forms of a class of inequalities of G. Pólya-G. Szegö, and L. V. Kantorovich, Bull. Amer. Math. Soc., 69(1963) 415-418.
[5] M. V. Diudea, QSPR/QSAR studies by molecular descriptors, NOVA, New York, 2001.
[6] F. FalahatiNezhad, A. Iranmanesh, A. Tehranian and M. Azari, Strict lower bounds on the multiplicative Zagreb indices of graph operations, ArsCombin., 117(2014) 399-409.
[7] F. Falahati-Nezhad, M. Azari. Bounds on the hyper-Zagreb index, J. Appl. Math. Inform., 34(2016), 319-330.
[8] F. Falahati-Nezhad, A. Iranmanesh, A. Tehranian and M. Azari, Comparing the second multiplicative Zagreb coindex with some graph invariants, Trans. Comb., 3(4) (2014) 31-41.
[9] F. FalahatiNezhad, M. Azari andT. Došlić, Sharp bounds on the inverse sum indegindex, Discrete Applied Mathematics, 217 (2017) 185-195.
[10] F. Falahati-Nezhad, A. Iranmanesh, A. Tehranian and M. Azari, Upper bounds on the second multiplicative Zagreb coindex, Util. Math., 96 (2015) 79-88.
[11] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53(4) (2015) 1184–1190.
[12] I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986.
[13] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals, Total electronenergy of alternant hydrocarbons, Chem. Phys. Lett., 17 (1972) 535-538.
[14] A. Ilić, G. Yu and L. Feng, On the eccentric distance sum of graphs, J. Math. Anal. Appl., 381(2011) 590–600.
[15] A. Miličević, S. Nikolić, N. Trinajstić, On reformulated Zagreb indices, Mol. Divers.8399-3930 (2004).
[16] M. Randić, On characterization of molecular branching, J. Am. Chem. Soc., 97 (1975) 6609-6615.
[17] V. Sharma, R. Goswami and A. K. Madan, Eccentric connectivity index: A novel highly discriminating topological descriptor for structure–property and structure–activity studies, J. Chem. Inf. Comput. Sci., 37 (1997) 273–282.
[18] G. H. Shirdel, H. Rezapour and A. M. Sayadi, The hyper-Zagreb index of graph operations, Iranian J. Math. Chem., 4(2) (2013) 213-220.
[19] D. Vukičević and B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem., 46 (2009) 1369-1376.
[20] D. Vukičević, M. Gašperov, Bond additive modeling 1. Adriatic indices, Croat. Chem. Acta83 (2010) 243–260.