Bounds for symmetric division deg index of graphs

Abstract

Let $G=(V,\,E)$ be a simple connected graph of order $n\,(\geq 2)$
and size $m$, where $V(G)=\{1,\,2,\ldots,\,n\}$. Also let
$\Delta=d_1\geq d_2\geq\cdots\geq d_n=\delta>0$, $d_i=d(i)$, be a
sequence of its vertex degrees with maximum degree $\Delta$ and
minimum degree $\delta$. With $SDD=\sum_{i\sim
j}\frac{d_i^2+d_j^2}{2d_id_j}$ we denote symmetric division deg
index, where $i\sim j$ means that vertices $i$ and $j$ are adjacent.
In this paper we give some new bounds for this topological index.
Moreover, we present a relation between topological indices of
graph.