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.

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. 
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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},
     publisher = {mathdoc},
     volume = {40},
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     year = {2015},
     url = {http://geodesic.mathdoc.fr/item/BASS_2015_40_1_a2/}
}
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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/