The F–Index for some Special Graphs and some Properties of the F–Index

Document Type: Research Paper


1 Department of Mathematics, Science and Research Branch, Islamic Azad University, P. O. Box 14515 – 1775, Tehran, Iran

2 Tarbiat Modares University

3 Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia

4 Islamic Azad University


The "forgotten topological index" or "F–index" has been introduced by Furtula and Gutman in 2015. The F–index of a (molecular) graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we compute this topological index for some special graphs such as Wheel graph, Barbell graph and Friendship graph. Moreover, the effects on the F–index are observed when some operations such as edge switching, edge moving and edge separating are applied to the graphs. Finally, we investigate degeneracy of F–index for small graphs.


Main Subjects

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