I am working on proving the NP-hardness of a problem by reducing it from the subgraph isomorphism problem. Currently, I can reduce it from the following problem:

**Problem 1:** Given two graphs $G=(V, E)$ and $H=(V’, E’)$, is there a subgraph $G_0$ of $G$ that is isomorphism to $H$ under a **linear mapping of vertices**?

But the original subgraph isomorphism problem is defined as:

**Problem 2:** Given two graphs $G=(V, E)$ and $H=(V’, E’)$, is there a subgraph $G_0$ of $G$ that is isomorphism to $H$ under a **bijection of vertices**?

Can anybody tell me how to further reduce Problem 1 from Problem 2?