Realization for tensor products of Leavitt path algebras

For two given graphs, we construct an augmentation graph. We obtain an injective algebra homomorphism from the Leavitt path algebra of the augmentation graph to the tensor product of the Leavitt path algebras of the given graphs, and give a necessary and sufficient condition on the surjectivity of the homomorphism. This gives rise to a realization of the tensor product of two Leavitt path algebras as a Leavitt path algebra.