K_{2,n} and K_{3,n} are stable, K_{m,m+k} is stable for large m with fixed gap k, and K_{m,ℓm} is unstable for rational ℓ>1 and large m.
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The stability of independence polynomials of complete bipartite graphs
K_{2,n} and K_{3,n} are stable, K_{m,m+k} is stable for large m with fixed gap k, and K_{m,ℓm} is unstable for rational ℓ>1 and large m.