On the reciprocal augmented Sombor index

The reciprocal augmented Sombor (RASO) index is a recently introduced vertex-degree-based graph invariant whose mathematical properties have not yet been exclusively investigated. In this paper, we present the first comprehensive study of this index. We derive sharp bounds for the RASO index in terms of fundamental graph parameters, including the order, size, minimum degree, and maximum degree of a graph. We further characterize the graphs minimizing/maximizing the RASO index among all fixed-order (ⅰ) connected graphs, (ⅱ) trees, and (ⅲ) unicyclic graphs. In addition, we examine the effect of edge addition on the RASO index and establish conditions under which this operation increases its value.