Constructing the $r$-uniform supertrees with the same spectral radius and matching energy

Abstract

  An $r$-uniform supertree is a connected and acyclic hypergraph of which each edge has $r$ vertices, where $r\geq 3$.  We propose the concept of matching energy for an $r$-uniform hypergraph, which is  defined as  the sum of the absolute value of all the eigenvalues of its matching polynomial.   With the aid of the matching polynomial of an $r$-uniform supertree,  three pairs of $r$-uniform supertrees with the same spectral radius \textcolor{black}{and the same matching energy} are  constructed, and two  infinite families of $r$-uniform supertrees with the same spectral radius \textcolor{black}{and the same  matching energy} are characterized. Some known results about the graphs with the same spectra regarding to their adjacency matrices can be  naturally deduced from our new results.