Some properties of the novel topological graph index Atom-Bond Sum-Connectivity index

The sum-connectivity variant of atom-bond connectivity index is recently introduced, and is defined as the sum of the terms of the form √(dᵤ+dᵥ-2)/(dᵤ+dᵥ) over all adjacent vertices $u, v$ in a graph G, and named as the atom-bond sum connectivity index denoted by $ABS(G)$. The sum of the absolute values of all the eigenvalues of the adjacency matrix of a graph G is known as the graph energy $E(G)$. In this paper, we observe some mathematical properties of $ABS(G)$ and establish bounds for this index in terms of other indices. We also compare $ABS(T)$ with $E(T)$ taking all trees T of order n=8,9,⋯,14 and observe a very strong correlation between the two invariants for all studied groups of trees.\\ Keywords: Atom-Bond Sum-Connectivity index, ABS, topological index, graph energy\\ MSC 2010 Codes: 05C07, 05C50 MSC 2010 Codes: 05C07, 05C50