Geodesic
Lower Bounds for Inverse Sum Indeg Index of Graphs
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 551

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Let $G=(V,E)$, $V=\{1,2,\ldots,n\}$, be a simple connected graph with $n$ vertices and $m$ edges and let $d_1\geq d_2\geq\cdots\geq d_n>0$, be the sequence of its vertex degrees. With $i\sim j$ we denote the adjacency of the vertices $i$ and $j$ in $G$. The inverse sum indeg index is defined as $ISI=\sum \frac{d_i\,d_j}{d_i+d_j}$ with summation going over all pairs of adjacent vertices. We consider lower bounds for $ISI$. We first analyze some lower bounds reported in the literature. Then we determine some new lower bounds.
Classification : 05C12 05C50
Keywords: degree (of vertex), degree (of edge), inverse sum indeg index, Zagreb index 
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     title = {Lower {Bounds} for {Inverse} {Sum} {Indeg} {Index} of {Graphs}},
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I. Gutman; M. Matejić; E. Milovanović; I. Milovanović. Lower Bounds for Inverse Sum Indeg Index of Graphs. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 4, p. 551 . http://geodesic.mathdoc.fr/item/KJM_2020_44_4_a5/