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We consider a family of quantum graphs$\{(\Gamma,\mathcal{A}_\varepsilon)\}_{\varepsilon>0}$, where $\Gamma$ is a$\mathbb{Z}^n$-periodic metric graph and the periodic Hamiltonian$\mathcal{A}_\varepsilon$ is defined by the operation $-\varepsilon^{-1}{\mathrm{d} ^2\over \mathrm{d} x^2}$ on the edges of $\Gamma$ and either$\delta'$-type conditions or the Kirchhoff conditions at its vertices. Here$\varepsilon>0$ is a small parameter. We show that the spectrum of$\mathcal{A}_\varepsilon$ has at least $m$ gaps as $\varepsilon\to 0$($m\in\mathbb{N}$ is a predefined number), moreover the location of these gapscan be nicely controlled via a suitable choice of the geometry of $\Gamma$ andof coupling constants involved in $\delta'$-type conditions.

Gaps in the spectrum of a periodic quantum graph with periodically distributed $\delta'$-type interactions