Probabilistic analysis of the first Zagreb index

Document Type : Research Paper


Department of statistics, Imam Khomeini International University, Qazvin


In this paper we study the first Zagreb index in bucket recursive trees containing buckets with variable‎ ‎capacities‎. ‎This model was introduced by Kazemi in 2012‎. ‎We‎ ‎obtain the mean and variance of the first Zagreb index and‎
‎introduce a martingale based on this quantity‎.


Main Subjects

P. Billingsley (1995). Probability and Measure. A Wiley-Interscience Publication, John Wiley and Sons, Inc., New York. J. Devillersand and A. T. Balaban (1999). Topological indices and related descriptors in QSAR and QSPR. Gordon and Breach, Amsterdam. I. Gutman and N. Trinajstic (1972). Graph theory and molecular orbitals. Total $\varphi$-electron energy of alternant hydrocarbons. Chem. Phys. Lett.. 17, 535-538 M. Kuba and A. Panholzer (2010). A Combinatorial approach to the analysis of bucket recursive trees. Theoret. Comput. Sci.. 411 (34-36), 3255-3273 H. Mahmoud and R. Smythe (1995). Probabilistic analysis of bucket recursive trees. Theoret. Comput. Sci.. 144, 221-249 S. Nikolic, I. M. Tolic, N. Trinajstic and I. Baucc (2000). On the Zagreb indices as complexity indices. Croatica Chemica Acta.. 73, 909-921 S. Nikolic, G. Kovacc, A. Milicc and N. Trinajstic (2003). On molecular complexity indices, In Complexity in Chemistry: Introduction and Fundamentals. eds D. Bonchev and D. H. Rouvray, Taylor and Francis, London. , 29-89 R. Kazemi (2013). Depth in bucket recursive trees with variable capacities of buckets. Acta Math. Sin. Engl. Ser., DOI: X. Li, Z. Li and L. Wang (2003). The inverse problems for some topological indices in combinatorial chemistry. J. Comput. Biol.. 10, 47-55