Gupta, C. K.; Lokesha, V.; Shwetha, Shetty B.; Ranjini, P. S. On the symmetric division deg index of graph. (English) Zbl 1363.05043 Southeast Asian Bull. Math. 40, No. 1, 59-80 (2016). Summary: The symmetric division deg index (SDD) is one of the 148 discrete Adriatic indices, it is a good predictor of total surface area for polychlorobiphenyls. The symmetric division deg index of a connected graph \(G\), is defined as \(\mathrm{SDD}(G)=\sum_{uv\in E(G)}\frac{d_u}{d_v}+\frac{d_v}{d_u}\) where \(d_v\) is the degree of a vertex \(v\) in \(G\). In this paper, we provide a lower and upper bounds of symmetric division deg index of connected graphs. Also, we establish the Nordhaus-Gaddum-type relations for symmetric division deg index of a connected graph, unicyclic and bicyclic graph. Cited in 25 Documents MSC: 05C07 Vertex degrees 05C35 Extremal problems in graph theory 05C40 Connectivity Keywords:Graph operations symmetric division deg index; maximum degree; pendent vertices; unicyclic graphs; bicyclic graphs PDFBibTeX XMLCite \textit{C. K. Gupta} et al., Southeast Asian Bull. Math. 40, No. 1, 59--80 (2016; Zbl 1363.05043)