Let \( G \) be a graph of minimum degree at least \( 1 \). Denote by \( d_i \) the degree of a vertex \( v_i \) in \( G \). The notation \( i\nsim j \) is used to indicate that the vertices \( v_i \) and \( v_j \) are not adjacent in \( G \). A graph of maximum degree at most 4 is known as a molecular graph. A connected graph having the same order and size is called a unicyclic graph. The symmetric division deg coindex of \( G \) is defined as \( \overline{SDD}(G) =\sum_{i\nsim j;v_i\ne v_j} (d_i^2+d_j^2)(d_id_j)^{-1} \). In this paper, new bounds for the coindex \( \overline{SDD}(G) \) as well as relations between \( \overline{SDD}(G) \) and some other topological indices/coindices are obtained. From one of the obtained results, it follows that the star graph (cycle graph, respectively) uniquely minimizes symmetric division deg coindex among all trees ((molecular) unicyclic graphs, respectively) of a given order.