Geodesic
On an old/new degree-based topological index
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 40 (2015) no. 1 
Boris Furtula; Ivan Gutman; Žana Kovijanić Vukićević; Giorgi Lekishvili; Goran Popivoda. On an old/new degree-based topological index. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 40 (2015) no. 1. http://geodesic.mathdoc.fr/item/BASS_2015_40_1_a2/
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     author = {Boris Furtula and Ivan Gutman and \v{Z}ana Kovijani\'c Vuki\'cevi\'c and Giorgi Lekishvili and Goran Popivoda},
     title = {On an old/new degree-based topological index},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {19 - 31},
     year = {2015},
     volume = {40},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BASS_2015_40_1_a2/}
}
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Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $G$ be a graph with vertex sex $V(G)$ and let $d(x)$ be the degree of the vertex $x \in V(G)$. The graph invariant $F = \sum\limits_{x \in V(G)} d(x)^3$ played some role in a paper published in 1972, but has not attracted any attention until quite recently. In 2014 an unexpected chemical application of the $F$-index was discovered, which motivated us to establish its basic mathematical properties. Results obtained along these lines are presented.