  The Sombor index (SO) is a vertex-degree-based graph invariant, defined as
the sum over all pairs of adjacent vertices of $\sqrt{d_i^2+d_j^2}$, where
$d_i$ is the degree of the $i$-th vertex. It has been conceived using geometric
considerations. Recently, a series of new SO-like degree-based graph invariants
(denoted by $SO_1, SO_2,..., SO_6$) is taken into consideration, when the
geometric background of several classical topological indices (Zagreb,
Albertson) has considered. In this paper, we compute and study these new
indices for some graphs, cactus chains and polymers.
