  In this article, we explore the concept of spectral redundancy within the
class of pineapple graphs, denoted as $\mathcal{P}(\alpha,\beta)$. These graphs
are constructed by attaching $\beta$ pendent edges to a single vertex of a
complete graph $K_\alpha$. A connected graph $G$ earns the title of being
spectrally non-redundant if the spectral radii of its connected induced
subgraphs remain distinct. Spectral redundancy, on the other hand, arises when
there is a repetition of spectral radii among the connected induced subgraphs
within $G$. Specifically, we analyze the adjacency spectrum of
$\mathcal{P}(\alpha,\beta)$, revealing distinct eigenvalues including $0$,
$-1$, and additional eigenvalues, some negative and others positive. Our
investigation focuses on determining the spectral redundancy within this class
of graphs, shedding light on their unique structural properties and
implications for graph theory.
