More path/walk/trail notes.
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"graph-isomorphic.png",
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"graph-isomorphic.png",
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"graph-induced-subgraph.png",
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"graph-induced-subgraph.png",
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"graph-subgraph.png",
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"graph-subgraph.png",
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"graph-non-subgraph.png"
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"graph-non-subgraph.png",
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"cyclic-undirected-labelled.png"
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],
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],
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"File Hashes": {
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"ontology/philosophy/properties.md": "41b32249d3e4c23d73ddb3a417d65a4c"
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"fields_dict": {
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---
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title: "2024-08-19"
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---
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- [ ] Anki Flashcards
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- [x] KoL
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- [ ] OGS
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- [ ] Sheet Music (10 min.)
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- [ ] Korean (Read 1 Story)
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@ -1201,6 +1201,42 @@ Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (
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<!--ID: 1710807788538-->
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<!--ID: 1710807788538-->
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END%%
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END%%
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%%ANKI
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Basic
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With maximum specificity, is $\langle B, D, E, J, K, B, A \rangle$ a path, trail, or walk?
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![[cyclic-undirected-labelled.png]]
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Back: A trail.
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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).
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<!--ID: 1723995290880-->
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END%%
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%%ANKI
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Basic
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With maximum specificity, is $\langle B, D, E, J, K, B \rangle$ a path, trail, or walk?
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![[cyclic-undirected-labelled.png]]
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Back: A path.
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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).
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<!--ID: 1723995290889-->
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END%%
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%%ANKI
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Basic
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With maximum specificity, is $\langle B, D, B, K, L \rangle$ a path, trail, or walk?
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![[cyclic-undirected-labelled.png]]
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Back: A walk.
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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).
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<!--ID: 1723995290893-->
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END%%
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%%ANKI
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Basic
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With maximum specificity, is $\langle A, B, D \rangle$ a path, trail, or walk?
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![[cyclic-undirected-labelled.png]]
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Back: A path.
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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).
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<!--ID: 1723995290896-->
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END%%
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## Isomorphisms
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## Isomorphisms
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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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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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