Is there any well-defined symbol to denote the difference between the two graphs. The difference between two graphs $G$ and $H$ is defined as the remaining sub-graph $G'$ of $G$ after the subgraph $H$ is removed from $G$ (assuming $H$ is a sub-graph of $G$). For example (the image is taken from Wolfram):
Note that, $G'$ might not be unique, since $H$ can be positioned anywhere in $G$, Although I can define my own symbol, it would be better to use the symbol that is well defined by the community.
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Best Answer
If you use notation $G-H$ or $G\setminus H$, it will often be interpreted as taking the graph $G$ and removing from it all the vertices of $H$ and any edge incident with a vertex of $H$. Which is not what you want.
The easiest way to write this would probably be $G-E(H)$, as this makes it clear you are only removing edges, and is unambiguous.
Alternatively, you could just define your own symbol / notation and state what it means up front, this is perfectly acceptable so long as you give a clear definition.