We propose a new topological vertex formalism for a type IIB $(p,q)$ 5-brane web with an O5-plane. We apply our proposal to five-dimensional N=1 Sp(1) gauge theory with Nf=0, 1, 8 flavors to compute the topological string partition functions and check the agreement with the known results. Especially for the Nf=8 case, which corresponds to E-string theory on a circle, we obtain a new, yet simple, expression of the partition function with a two Young diagram sum.
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Kim et al. (2018) studied this question.