For n≥8(r^2+r+4), the unique spectral extremal non-bipartite B_{r+1}-free graph of order n is the nearly balanced complete bipartite graph with one added vertex adjacent to r vertices in each part.
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Spectral Tur\'{a}n problem of non-bipartite graphs: Forbidden books
For n≥8(r^2+r+4), the unique spectral extremal non-bipartite B_{r+1}-free graph of order n is the nearly balanced complete bipartite graph with one added vertex adjacent to r vertices in each part.