University of Isfahan Transactions on Combinatorics 2251-8657 13 3 2024 09 01 The minimum $\varepsilon$-spectral radius of $t$-clique trees with given diameter 235 255 27700 10.22108/toc.2023.134435.2002 EN Zhengping Qiu School of Computational Science and Electronics, Hunan Institute of Engineering, Xiangtan,411104, P. R. China. Hanyuan Deng College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, P. R. China Zikai Tang School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China. Journal Article 2022 07 16 The eccentricity matrix $\varepsilon(G)$ of a graph $G$ is defined as \begin{equation}<br />\varepsilon(G)_{uv}= \begin{cases}<br />d_{uv} & d_{uv}=min\{e(u),e(v)\},\\<br />0 & d_{uv} < min\{e(u),e(v)\}. \notag<br />\end{cases}<br />\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. https://toc.ui.ac.ir/article_27700_9ea030450559b7d7e48773a826aae421.pdf