Sharp bounds on the symmetric division deg index of graphs and line graphs

For a graph G with vertex set VG and edge set EG, the symmetric division deg index is defined as SDD(G) = Sigma(uv epsilon) E-G ( du /dv + dv/du), where du denotes the degree of vertex u in G. In 2018, Furtula et al. confirmed the quality of SDD index exceeds that of some more popular VDB indices, in particular that of the GA index. They show a close connection between the SDD index and the earlier well-established GA index. Thus, it is meaningful and important to consider the chemical and mathematical properties of the SDD index. In this paper, we determine some sharp bounds on the symmetric division deg index of graphs and line graphs and characterize the corresponding extremal graphs.