Tree with the Extremal Value of Exponential the Forgotten Index

EasyChair Preprint 6866

Abstract

For simple graph $G$ with edge set $E(G)$, $e^{\mathcal{F}_\alpha}(G)=\sum_{uv\in E(G)}e^{d^\alpha_G(u)+d^\alpha_G(v)}$, where $d_G(u)$ is the degree of the vertex $u$ in $G$, ~$\alpha\neq0$ is real. When $\alpha=2$, $e^\mathcal{F}(G)=e^{\mathcal{F}_2}(G)$ is called exponential forgotten index of $G$. In this paper, we first give the extremal value of exponential forgotten index of tree and determine the corresponding extremal graphs. Furthermore, we give the extremal values of exponential index $e^{\mathcal{F}_\alpha}$ of trees, where $\alpha>1$ and determine the corresponding extremal graphs.

Keyphrases: Exponential forgotten index, Extremal tree, Extremal value, tree

@booklet{EasyChair:6866,
  author    = {Mingyao Zeng and Hanyuan Deng},
  title     = {Tree with the Extremal Value of Exponential the Forgotten Index},
  howpublished = {EasyChair Preprint 6866},
  year      = {EasyChair, 2021}}