Geodesic
On the Difference Between Atom-Bond Sum-Connectivity and Sum-Connectivity Indices
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 47 (2022) no. 1 
Kalkere Jayanna Gowtham; Ivan Gutman. On the Difference Between Atom-Bond Sum-Connectivity and Sum-Connectivity Indices. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 47 (2022) no. 1. http://geodesic.mathdoc.fr/item/BASS_2022_47_1_a3/
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     title = {On the {Difference} {Between} {Atom-Bond} {Sum-Connectivity} and {Sum-Connectivity} {Indices}},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {55 - 5},
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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

The atom-bond sum-connectivity index $ABS$ is a recently introduced vertex-degree-based graph invariant, defined as the sum over all pairs of adjacent vertices $u,v$ of the term $\sqrt{(d_u+d_v-2)/(d_u+d_v)}$, where $d_u$ is the degree of the vertex $u$. A much older such invariant, the sum-connectivity index $SC$, is defined via $\sqrt{(1/(d_u+d_v)}$. We study the difference between $ABS$ and $SC$ and establish various bounds for it, in terms several vertex-degree-based graph invariants.