More path/walk/trail notes.

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Joshua Potter 2024-08-19 07:45:06 -06:00
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---
title: "2024-08-19"
---
- [ ] Anki Flashcards
- [x] KoL
- [ ] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)

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<!--ID: 1710807788538-->
END%%
%%ANKI
Basic
With maximum specificity, is $\langle B, D, E, J, K, B, A \rangle$ a path, trail, or walk?
![[cyclic-undirected-labelled.png]]
Back: A trail.
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: 1723995290880-->
END%%
%%ANKI
Basic
With maximum specificity, is $\langle B, D, E, J, K, B \rangle$ a path, trail, or walk?
![[cyclic-undirected-labelled.png]]
Back: A path.
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: 1723995290889-->
END%%
%%ANKI
Basic
With maximum specificity, is $\langle B, D, B, K, L \rangle$ a path, trail, or walk?
![[cyclic-undirected-labelled.png]]
Back: A walk.
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: 1723995290893-->
END%%
%%ANKI
Basic
With maximum specificity, is $\langle A, B, D \rangle$ a path, trail, or walk?
![[cyclic-undirected-labelled.png]]
Back: A path.
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: 1723995290896-->
END%%
## Isomorphisms
An **isomorphism** between two graphs $G_1$ and $G_2$ is a bijection $f \colon V_1 \rightarrow V_2$ between the vertices of the graphs such that $(a, b)$ is an edge in $G_1$ if and only if $(f(a), f(b))$ is an edge in $G_2$. Here parenthesis are used to denote either ordered pairs (for directed graphs) or unordered pairs (for undirected graphs).

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