Abstract:

For a simple graph $G$ with edge set $E(G)$, the exponential inverse forgotten index of $G$ is defined as ~$e^{\frac{1}{\mathcal{F}}}(G)=\sum_{uv\in E(G)}e^{\left(\frac{1}{{d_G^2(u)}}+\frac{1}{{d_G^2(v)}}\right)}$, where $d_G(u)$ is the degree of the vertex $u$ in $G$. In this paper, firstly, we give the minimum value of exponential inverse forgotten index of a tree and determine its corresponding extremal graph. Then, we investigate the maximum value of the exponential inverse forgotten index and describe the structural characteristics of the extremal graph. 

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