On Harary Matrix, Harary Index and Harary Energy

Recently, a new molecular graph matrix, Harary matrix, was defined in honor of Professor Frank Harary, and new graph invariants (local and global) based on it were also defined and researched, Harary index is one of these invariants. The Harary matrix can be used to derive a variant of the Balaban index, Harary index was also successfully tested in several structure-property relationships, so it is very meaningful to research their mathematical properties and chemical applications. As a class of graph energy, Harary energy was introduced not long ago. In this paper, we obtain some results about eigenvalues of Harary matrix, then by these results, we get some bounds of Harary index. Moreover, we obtain some bounds of Harary energy.