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Recently, the ATLAS and CMS Collaborations reported the latest experimentalupper limits on the branching ratios of the lepton flavor violating (LFV) 125GeV Higgs boson decays, $h\rightarrow e\mu$, $h\rightarrow e\tau$, and$h\rightarrow \mu\tau$. In this paper, we mainly investigate the LFV Higgsboson decays $h\rightarrow e\mu$, $h\rightarrow e\tau$, and $h\rightarrow\mu\tau$ in the minimal supersymmetric extension of the Standard Model withlocal $\emph{B-L}$ gauge symmetry. At the same time, the correspondingconstraints from the LFV rare decays $\mu\rightarrow e\gamma$, $\tau\rightarrowe\gamma$, $\tau\rightarrow \mu\gamma$, and muon $(g-2)$ are considered toanalyze the numerical results.

Higgs boson decays with lepton flavor violation in the $B-L$ symmetric SSM