Notes on graphs and git remotes.

notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json

@@ -124,7 +124,10 @@
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     "array-multi-row-major.png",
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+    "graph-induced-subgraph.png",
+    "graph-subgraph.png",
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notes/_journal/2024-05-13.md

@@ -6,4 +6,7 @@ title: "2024-05-13"
 - [x] KoL
 - [ ] Sheet Music (10 min.)
 - [ ] Go (1 Life & Death Problem)
-- [ ] Korean (Read 1 Story)
+- [ ] Korean (Read 1 Story)
+
+* Notes on [[graphs#Subgraphs|subgraphs]] and induced subgraphs.
+* Notes on [[remotes]].

notes/git/refs.md

@@ -11,7 +11,7 @@ tags:
 A **reference** (or **ref**) is essentially a file containing an oid. The name of the file can then be used to reference the oid. A **symbolic reference** is a file containing the name of another reference. The primary refs are:
 
 * heads (i.e. branches)
-* remotes (i.e. remote branches)
+* [[remotes]] (i.e. remote branches)
 * [[objects#Tags|tags]]
 
 %%ANKI

notes/git/remotes.md

@@ -0,0 +1,59 @@
+---
+title: Remotes
+TARGET DECK: Obsidian::STEM
+FILE TAGS: git
+tags:
+  - git
+---
+
+## Overview
+
+A **remote** is a version of the project different from the one currently on. Remotes are stored in `.git/config`. List remotes using the following command:
+
+```sh
+$ git remote -v
+```
+
+%%ANKI
+Basic
+What is a remote repository?
+Back: A version of the repository located *somewhere* else.
+Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
+<!--ID: 1715623927181-->
+END%%
+
+%%ANKI
+Basic
+What misnomer may be associated with a remote repository?
+Back: A remote could exist on the same machine as the referencing repo.
+Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
+<!--ID: 1715623927187-->
+END%%
+
+%%ANKI
+Basic
+Where are git remotes specified within the `.git` directory?
+Back: In `.git/config`
+Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
+<!--ID: 1715623927191-->
+END%%
+
+%%ANKI
+Basic
+What two properties are initialized when creating a new git remote?
+Back: The URL and fetch refspec.
+Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
+<!--ID: 1715623927194-->
+END%%
+
+%%ANKI
+Basic
+What kind of git refs are associated with remotes?
+Back: Remote branch refs.
+Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
+<!--ID: 1715623927197-->
+END%%
+
+## Bibliography
+
+* Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).

notes/set/graphs.md

@@ -1149,6 +1149,147 @@ Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n
 <!--ID: 1715543813492-->
 END%%
 
+## Subgraphs
+
+We say $G' = (V', E')$ is a **subgraph** of $G = (V, E)$ provided $V' \subseteq V$ and $E' \subseteq E$. We say $G' = (V', E')$ is an **induced subgraph** of $G = (V, E)$ provided $V' \subseteq V$ and every edge in $E$ whose vertices are still in $V'$ is also an edge in $E'$.
+
+%%ANKI
+Basic
+What *is* a subgraph of $G = (V, E)$?
+Back: A graph $G' = (V', E')$ such that $V' \subseteq V$ and $E' \subseteq E$.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715619756612-->
+END%%
+
+%%ANKI
+Basic
+What *is* an induced subgraph of $G = (V, E)$?
+Back: A graph $G' = (V', E')$ such that $V' \subseteq V$ and every edge in $E$ whose vertices are in $V'$ is in $E'$.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715619756617-->
+END%%
+
+%%ANKI
+Basic
+Which of subgraphs or induced subgraphs are more general?
+Back: Subgraphs.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715619756621-->
+END%%
+
+%%ANKI
+Basic
+Is an induced subgraph a subgraph?
+Back: Yes.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715619756626-->
+END%%
+
+%%ANKI
+Basic
+Is a subgraph an induced subgraph?
+Back: Not necessarily.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715619756630-->
+END%%
+
+%%ANKI
+Basic
+How can deletion be used to create a subgraph from a graph?
+Back: By deleting vertices (with connected edges) as well as any additional edges.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715619756634-->
+END%%
+
+%%ANKI
+Basic
+How can deletion be used to create an induced subgraph from a graph?
+Back: By only deleting vertices and their connected edges.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715619756637-->
+END%%
+
+%%ANKI
+Basic
+Is the second graph a subgraph of the first?
+![[graph-induced-subgraph.png]]
+Back: Yes.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715620447931-->
+END%%
+
+%%ANKI
+Basic
+Is the second graph an induced subgraph of the first?
+![[graph-induced-subgraph.png]]
+Back: Yes.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715620447935-->
+END%%
+
+%%ANKI
+Basic
+Is the second graph a subgraph of the first?
+![[graph-subgraph.png]]
+Back: Yes.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715620447939-->
+END%%
+
+%%ANKI
+Basic
+Is the second graph an induced subgraph of the first?
+![[graph-subgraph.png]]
+Back: No.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715620447942-->
+END%%
+
+%%ANKI
+Basic
+Why isn't the second graph an induced subgraph of the first?
+![[graph-subgraph.png]]
+Back: The second graph is missing edge $\{a, b\}$.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715620447946-->
+END%%
+
+%%ANKI
+Basic
+Is the second graph a subgraph of the first?
+![[graph-non-subgraph.png]]
+Back: No.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715620447949-->
+END%%
+
+%%ANKI
+Basic
+Why isn't the second graph a subgraph of the first?
+![[graph-non-subgraph.png]]
+Back: Edge $\{c, f\}$ is not in the first graph.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715620447952-->
+END%%
+
+%%ANKI
+Basic
+Is the second graph an induced subgraph of the first?
+![[graph-non-subgraph.png]]
+Back: No.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715620447955-->
+END%%
+
+%%ANKI
+Basic
+Why isn't the second graph an induced subgraph of the first?
+![[graph-non-subgraph.png]]
+Back: Because the second graph isn't even a subgraph of the first.
+Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
+<!--ID: 1715620447958-->
+END%%
+
 ## Bibliography
 
 * Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).