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For a graph $G$ with vertex set $V_{G}$ and edge set $E_{G}$, the symmetricdivision deg index is defined as $SDD(G)=\sum\limits_{uv\inE_{G}}(\frac{d_{u}}{d_{v}}+\frac{d_{v}}{d_{u}})$, where $d_{u}$ denotes thedegree of vertex $u$ in $G$. In 2018, Furtula et al. confirmed the quality ofSDD index exceeds that of some more popular VDB indices, in particular that ofthe GA index. They shown a close connection between the SDD index and theearlier well-established GA index. Thus it is meaningful and important toconsider the chemical and mathematical properties of the SDD index. In thispaper, we determine some sharp bounds on the symmetric division deg index ofgraphs and line graphs and characterize the corresponding extremal graphs.

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