For a graph $G=(V,E)$, is there a standard notation for the induced subgraph on $V \setminus \{v,w\}$ where $v,w$ are the endpoints of some edge $e$? I know $G[V \setminus \{v,w\}]$ is an option, but I’m looking for something more compact. $G \setminus e$ is used for deletion and $G/e$ is used for contraction, so I’m inclined to use $G-e$, but perhaps that already has another meaning.
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asked Jun 28, 2020 at 23:00
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1$\begingroup$ Isn't $G-e$ used for the spanning subgraph where only the edge is deleted and the vertices remain? How about $G-u-v$? $\endgroup$– bofCommented Jun 28, 2020 at 23:15
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1$\begingroup$ Once I used $G-[e]$; page 38 here: arxiv.org/abs/1812.06627 $\endgroup$– Anton PetruninCommented Jun 28, 2020 at 23:16
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1$\begingroup$ As bof said, definitely do not used $G-e$ as that is extremely widespread as meaning that only the edge is removed and not its end-vertices. $\endgroup$– Brendan McKayCommented Jun 29, 2020 at 4:40
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$\begingroup$ I myself would probably use $G-\{v,w\}$ as I always avoid revealing the implementation of my edges as sets, that is, I never state that $e=\{v,w\}$. And then $G-S$ is equally well defined for any set $S$ of vertices. $\endgroup$– M. WinterCommented Jun 29, 2020 at 8:16
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