The minimum \varepsilon-spectral radius of t-clique trees with given diameter

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)\},\\۰ & 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-۱)t+۱ 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.

کلیدواژه ها:

Clique tree ، Diameter ، Minimal value ، Eccentricity matrix ، \varepsilon-spectra