Stirling Numbers and Generalized Zagreb Indices

Document Type: Research Paper


1 1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb,

2 Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, Iran

3 Department of Mathematics, Babol Branch, Islamic Azad University, Babol, Iran


We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.


Main Subjects

1. E. Deutsch, S. Klavžar, M–polynomial and degree–based topological indices,
Iranian J. Math. Chem. 6 (2015) 93–102.
2. T. Došlić, M. Ghorbani, M. A. Hosseinzadeh, Eccentric connectivity polynomial of
some graph operations, Util. Math. 84 (2011) 297–309.
3. G. H. Fath–Tabar, A. Azad, N. Elahinezhad, Some topological indices of tetrameric
1,3–adamantane, Iranian J. Math. Chem. 1 (2010) 111–118.
4. B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015)
5. R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison–Wesley,
Reading, 1988.
6. I. Gutman, K. Ch. Das, The first Zagreb index 30 years after, MATCH Commun.
Math. Comput. Chem. 50 (2004) 83–92.
7. I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total -electron
energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.
8. X. Li, J. Zheng, A unified approach to the extremal trees for different indices,
MATCH Commun. Math. Comput. Chem. 54 (2005) 195–208.
9. S. Sedghi, N. Shobe, M. A. Salahshoor, The polynomials of a graph, Iranian J.
Math. Sci. Inf. 3 (2008) 55–68.
10. G. B. A. Xavier, E. Suresh, I. Gutman, Counting relations for general Zagreb
indices, Kragujevac J. Math. 38 (2014) 95–103.