Graphs with Smallest Forgotten Index

Document Type : Research Paper

Authors

1 University of Kragujevac, Serbia

2 University of Kashan

Abstract

The forgotten topological index of a molecular graph G is defined as F(G)=\sum_{v\in V(G)}d^{3}(v), where d(u) denotes the degree of vertex u in G. The first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number \gamma=1,2, the first through the fourth for \gamma=3, and the first and the second for \gamma=4,5 are determined. These results are compared with those obtained for the first Zagreb index.

Keywords

Main Subjects

References

1. H. Abdo, D. Dimitrov, I. Gutman, On extremal trees with respect to the F-index,
Kuwait J. Sci., in press.
2. B. Basavanagoud, V. R. Desai, Forgotten topological index and hyper-Zagreb index
of generalized transformation graphs, Bull. Math. Sci. Appl. 14 (2016) 1–6.
3. N. De, S. M. A. Nayeem, A. Pal, F-index of some graph operations, Discrete Math.
Algorithm Appl. 8(2) (2016) 1650025.
4. B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015)
1184–1190.
5. B. Furtula, I. Gutman, Z. Kovijanić Vukićević, G. Lekishvili, G. Popivoda, On an
old/new degree–based topological index, Bull. Acad. Serbe Sci. Arts (Cl. Math.
Natur.) 40 (2015) 19–31.
6. I. Gutman, Degree–based topological indices, Croat. Chem. Acta 86 (2013) 351–
361.
7. I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun.
Math. Comput. Chem. 50 (2004) 83–92.
8. I. Gutman, B. Furtula, Z. Kovijanić Vukićević, G. Popivoda, On Zagreb indices and
coindices, MATCH Commun. Math. Comput. Chem. 74 (2015) 5–16.
9. I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total π-electron
energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.
10. X. Li, H. Zhao, Trees with the first three smallest and largest general topological
indices, MATCH Commun. Math. Comput. Chem. 50 (2004) 57–62.
11. S. Nikolić, G. Kovačević, A. Miličević, N. Trinajstić, The Zagreb indices 30 years
after, Croat. Chem. Acta 76 (2003) 113–124.
12. Y. M. Tong, J. B. Liu, Z. Z. Jiang, N. N. Lv, Extreme values of the first general
Zagreb index in tricyclic graphs, J. Hefei Univ. Nat. Sci. 1 (2010) 4–7.
13. S. Zhang, W. Wang, T. C. E. Cheng, Bicyclic graphs with the first three smallest
and largest values of the first general Zagreb index, MATCH Commun. Math.
Comput. Chem. 56 (2006) 579–592.
14. S. Zhang, H. Zhang, Unicyclic graphs with the first three smallest and largest first
general Zagreb index, MATCH Commun. Math. Comput. Chem. 55 (2006) 427–438.
Iranian Journal of Mathematical Chemistry
Volume 8, Issue 3
September 2017
Pages 259-273

Files

Share

How to cite

Statistics