Amin, Ruhul; Nayeem, Sk. Md. Abu Extremal \(F\)-index of a graph with \(k\) cut edges. (English) Zbl 1474.05209 Mat. Vesn. 72, No. 2, 146-153 (2020). 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. Cited in 1 Document MSC: 05C35 Extremal problems in graph theory 05C07 Vertex degrees 05C40 Connectivity 05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.) Keywords:\(F\)-index; cut edges; transformation × Cite Format Result Cite Review PDF Full Text: Link Link References: [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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.