Filomat 2024 Volume 38, Issue 1, Pages: 25-32
https://doi.org/10.2298/FIL2401025S
Full text (
286 KB)
Extremal reformulated forgotten index of trees, unicyclic and bicyclic graphs
Sarkar Ishita (Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India), ishita.sarkar@res.christuniversity.in
Nanjappa Manjunath (Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India), manjunath.nanjappa@christuniversity.in
Gutman Ivan 
(Faculty of Science, University of Kragujevac, Kragujevac, Serbia), gutman@kg.ac.rs
The reformulated forgotten index (RF) is the edge version of the ordinary
forgotten index. We describe graph transformations, by means of which RF
increases or decreases. Using these transformations, the trees, unicyclic,
and bicyclic graphs extremal w.r.t. RF are characterized.
Keywords: unicyclic graphs, trees, bicyclic graphs, reformulated forgotten index
Show references
S. Akhter, M. Imran, Computing the forgotten topological index of four operations on graphs, AKCE Int. J. Graphs Comb. 14 (2017), 70-79.
H. Aram, N. Dehgardi, Reformulated F-index of graph operations, Commun. Comb. Optim. 2 (2017), 87-98.
B. Borovićanin, K. C. Das, B. Furtula, I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem. 78 (2017), 17-100.
Z. Che, Z. Chen, Lower and upper bounds of the forgotten topological index, MATCH Commun. Math. Comput. Chem. 76 (2016), 635-648.
O. Colakoglu Havare, A. K. Havare, Computation of the forgotten topological index and co-index for carbon base nanomaterial, Polyc. Arom. Comp. 42 (2022), 3488-3500.
H. Deng, A unified approach to the extremal Zagreb indices for trees, unicyclic graphs and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 57 (2007), 597-616.
B. Furtula, I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), 1184-1190.
I. Gutman, K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83-92.
I. Gutman, E. Milovanović, I. Milovanović, Beyond the Zagreb indices, AKCE Int. J. Graphs Comb. 17 (2020), 74-85.
I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), 535-538.
S. Ji, X. Li, B. Huo, On reformulated Zagreb indices with respect to acyclic, unicyclic and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 72 (2014), 723-732.
J. Liu, M. Matejić, E. Milovanović, I. Milovanović, Some new inequalities for the forgotten topological index and coindex of graphs, MATCH Commun. Math. Comput. Chem. 84 (2020), 719-738.
D. Maji, G. Ghorai, F. A. Shami, The reformulated F-index of vertex and edge F-join of graphs, J. Chem. 2022 (2022), #2392109.
A. Miličević, S. Nikolić, N. Trinajstić, On reformulated Zagreb indices, Mol. Divers. 8 (2004), 393-399.
A. Rajpoot, L. Selvaganesh, Bounds and extremal graphs of second reformulated Zagreb index for graphs with cyclomatic number at most three, Kuwait J. Sci. 49 (2022), 1-21.
K. Xu, H. Hua, A unified approach to extremal multiplicative Zagreb indices for trees, unicyclic and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 68 (2012), 241-256.