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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):

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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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    $\begingroup$ given that union and complement are well defined, I think the natural suggestion is to use the \setminus for difference en.wikipedia.org/wiki/Graph_operations $\endgroup$ – Daniel S. Aug 16 '20 at 5:23
  • $\begingroup$ @DanielS. \setminus is for set difference right? So we can not use it for a graph $G = (V,E)$. $\endgroup$ – Inuyasha Yagami Aug 16 '20 at 6:30
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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.

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Based on the answer of @Brandon du Preez, we can also define the graph difference between $G$ and $H$, as $G'= (V',E')$, such that:

$V' = V(G)$, and $E' = E(G)-E(H)$

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    $\begingroup$ Please don't add "thank you" as an answer. Instead, accept the answer that you found most helpful. - From Review $\endgroup$ – José Carlos Santos Aug 19 '20 at 10:35
  • $\begingroup$ I have edited the answer. I wanted to point out another way to define the graph difference, based on the previous answer. $\endgroup$ – Inuyasha Yagami Aug 21 '20 at 6:03

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