A signed graph is determined by its adjacency spectrum (resp., Laplacian spectrum) if there is no other non-switching isomorphic signed graph having the same adjacency spectrum (resp., Laplacian spectrum). In particular, a starlike tree can also be interpreted as a signed graph. Oboudi On the eigenvalues and spectral radius of starlike trees, Aequationes Math. 92 (2018) 683–694 characterized all starlike trees whose adjacency eigenvalues are all in the interval Formula: see text, which are Formula: see text, Formula: see text, Formula: see text and Formula: see text for Formula: see text. In this paper, our focus is the problem of spectral determination of them. We prove that Formula: see text, Formula: see text, Formula: see text and Formula: see text for Formula: see text are determined by their adjacency spectra, and characterize all signed graphs which are non-switching isomorphic and adjacency cospectral with Formula: see text for other cases. Further, we show that Formula: see text, Formula: see text, Formula: see text and Formula: see text for Formula: see text are determined by their Laplacian spectra, and we characterize all signed graphs which are non-switching isomorphic and Laplacian cospectral to Formula: see text.
Zhou et al. (Fri,) studied this question.