Extremal \(F\)-index of a graph with \(k\) cut edges. (English) Zbl 1474.05209

Summary: The so called forgotten index or \(F\)-index is defined as the sum of cubes of vertex degrees of a molecular graph. In this paper, we have obtained the upper and lower bounds of \(F\)-index for the graphs with \(k\) cut edges and also we have characterized the extremal graphs.


05C35 Extremal problems in graph theory
05C07 Vertex degrees
05C40 Connectivity
05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.)
Full Text: Link Link


[1] H. Abdo, D. Dimitrov, I. Gutman,On extremal trees with respect to the F-index, Kuwait J. Sci.,44(2017), 1-8. · Zbl 1463.05071
[2] S. Chen, W. Liu,Extremal Zagreb indices of graphs with a given number of cut edges, Graphs Combin.,30(2014), 109-118. · Zbl 1292.05082
[3] B. Furtula, I. Gutman,A forgotten topological index, J. Math. Chem.,53(2015), 1184-1190. · Zbl 1317.05031
[4] I. Gutman, N. Trinajstic,Graph theory and molecular orbitals. Totalπ-electron energy of alternant hydrocarbons, Chem. Phys. Lett.,17(1972), 535-538.
[5] H. Liu, M. Lu, F. Tian,On the spectral radius of graphs with cut edges, Linear Algebra Appl., 389(2004), 139-145. · Zbl 1053.05080
[6] R. Amin, S. M. A. Nayeem,Ordering unicyclic graphs with respect to F-indices, arXiv: 1609.01128.
[7] Y.R. Wu, S. He, J. L. Shu,Largest spectral radius among graphs with cut edges, J. East China Norm. Univ. Nat. Sci. Ed.,3(2007), 67-74.
[8] Q. Zhao, S. C. Li,On the maximum Zagreb indices of graphs withkcut vertices, Acta Appl. Math.,111(2010), 93-106 · Zbl 1190.92050
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.