By means of first-principles calculations and modeling analysis, we have predicted that the traditional 2D-graphene hosts the topological phononic Weyl-like points (PWs) and phononic nodal line (PNL) in its phonon spectrum. The phonon dispersion of graphene hosts three type-I PWs (both PW1 and PW2 at the BZ corners emph{K} and emph{K}, and PW3 locating along the $Gamma$-emph{K} line), one type-II PW4 locating along the $Gamma$-emph{M} line, and one PNL surrounding the centered $Gamma$ point in the $q_{x,y}$ plane. The calculations further reveal that Berry curvatures are vanishingly zero throughout the whole BZ, except for the positions of these four pairs of Weyl-like phonons, at which the non-zero singular Berry curvatures appear with the Berry phase of $pi$ or -$pi$, confirming its topological non-trivial nature. The topologically protected non-trivial phononic edge states have been also evidenced along both the zigzag-edged and armchair-edged boundaries. These results would pave the ways for further studies of topological phononic properties of graphene, such as phononic destructive interference with a suppression of backscattering and intrinsic phononic quantum Hall-like effects.
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