@article {
author = {Qiu, Zhengping and Deng, Hanyuan and Tang, Zikai},
title = {The minimum $\varepsilon$-spectral radius of $t$-clique trees with given diameter},
journal = {Transactions on Combinatorics},
volume = {13},
number = {3},
pages = {235-255},
year = {2024},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2023.134435.2002},
abstract = {The eccentricity matrix $\varepsilon(G)$ of a graph $G$ is defined as \begin{equation}\varepsilon(G)_{uv}= \begin{cases}d_{uv} & d_{uv}=min\{e(u),e(v)\},\\0 & d_{uv} < min\{e(u),e(v)\}. \notag\end{cases}\end{equation} Let $T_t$ be a $t$-clique tree corresponding to the tree $T($underlying graph of $T_t)$ with order $n'=(n-1)t+1$ and diameter $d$. In this paper, we identify the extremal $t$-clique trees with given diameter having the minimum $\varepsilon$-spectral radius. Simultaneously, we calculate the lower bound of $\varepsilon$-spectral radius of $t$-clique trees when $n-d$ is odd.},
keywords = {Clique tree,Diameter,Minimal value,Eccentricity matrix,$\varepsilon$-spectra},
url = {https://toc.ui.ac.ir/article_27700.html},
eprint = {https://toc.ui.ac.ir/article_27700_9ea030450559b7d7e48773a826aae421.pdf}
}