In this paper, we study the monogamy inequality of Tsallis
q-entropy entanglement. We first provide an analytic formula of Tsallis
q-entropy entanglement in two-qubit systems for $\frac{5\ensuremath{-}\sqrt{13}}{2}\ensuremath{\le}q\ensuremath{\le}\frac{5+\sqrt{13}}{2}.$ The analytic formula of Tsallis
q-entropy entanglement in $2\ensuremath{\bigotimes}d$ system is also obtained and we show that Tsallis
q-entropy entanglement satisfies a set of hierarchical monogamy equalities. Furthermore, we prove the squared Tsallis
q-entropy entanglement follows a general inequality in the qubit systems. Based on the monogamy relations, a set of multipartite entanglement indicators is constructed, which can detect all genuine multiqubit entangled states even in the case of
N-tangle vanishes. Moreover, we study some examples in multipartite higher-dimensional system for the monogamy inequalities.
Tsallis-q entanglement is a bipartite entanglement measure which is the generalization of entanglement of formation for q tending to 1. We first expand the range of q for the analytic formula of Tsallis-q entanglement. For , we prove the monogamy relation in terms of the squared Tsallis-q entanglement for an arbitrary multi-qubit systems. It is shown that the multipartite entanglement indicator based on squared Tsallis-q entanglement still works well even when the indicator based on the squared concurrence loses its efficacy. We also show that the μ-th power of Tsallis-q entanglement satisfies the monogamy or polygamy inequalities for any three-qubit state.