### 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.

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