  We propose brane web configurations for $D$-type and $E$-type
$\mathcal{N}=(1,0)$ little string theories based on a trivalent or quadrivalent
gluing of 5-brane web diagrams. Tri-/quadri-valent gluing is a powerful way of
computing 5d/6d partition functions for supersymmetric gauge theories based on
the topological vertex. We generalize the gluing techniques to little string
theories by introducing a new compact direction and compute their
supersymmetric partition functions on Omega-deformed $\mathbb{R}^4\times T^2$.
As concrete examples, we consider little string theories arising from Type IIB
NS5-branes probing $D_4$ or $D_5$ singularity. Their effective gauge theory
descriptions as the affine $D_4$ or $D_5$ quiver gauge theory can be realized
with quadrivalent or trivalent gluing, respectively. Based on these gluings of
5-brane webs, we compute their refined partition functions and compare them
with the known results. We extend the computation of the partition function to
little string theory engineered from IIB NS5-branes probing $E_6$ singularity
based on a trivalent gluing. We also discuss the generalization to higher rank
cases and the symmetries of the partition functions.
