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A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. An H-shape is a tree with exactly two of its vertices having maximal degree 3. In this paper, a formula of counting the number of closed 6-walks is given on a graph, and some necessary conditions of a graph Γ cospectral to an H-shape are given.

On the Spectral Characterization of &lt;i&gt;H&lt;/i&gt;-Shape Trees

On the Spectral Characterization of <i>H</i>-Shape Trees