The Faber–Krahn inequality states that the first Dirichlet eigenvalue among all bounded domains is no less than a Euclidean ball with the same volume in \({\mathbb {R}}^n\) as reported (Chavel in Eigenvalues in Riemannian geometry, Academic Press, Orlando, FL, 1984). Bıyıkoğlu and Leydold (J Comb Theory Ser B 97:159–174, 2007) demonstrated that the Faber–Krahn inequality also holds for the class of trees with boundary with the same degree sequence and characterized the unique extremal tree. Bıyıkoğlu and Leydold (J Comb Theory Ser B 97:159–174, 2007) also posed a question as follows: Give a characterization of all graphs in a given class \({\mathcal {C}}\) with the Faber–Krahn property. In this paper, we address this question specifically for k-uniform supertrees with boundary. We introduce a spiral-like ordering (SLO-ordering) of vertices for supertrees, an extension of the SLO-ordering for trees initially proposed by Pruss (Duke Math J 91:463–514, 1998), and prove that the SLO-supertree has the Faber-Krahn property among all supertrees with a given degree sequence. Furthermore, among degree sequences that have a minimum degree d for interior vertices, the SLO-supertree with degree sequence \((d,\ldots ,d, d', 1, \dots , 1)\) possesses the Faber-Krahn property.
