Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2604.23379 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910166248587264 |
|---|---|
| author | Ates, Lillian Chapman, Zachary Estes, John Jackson, Tyler |
| author_facet | Ates, Lillian Chapman, Zachary Estes, John Jackson, Tyler |
| contents | For a graph $G$ and vertices $u,v$, we define the ASUA of $v$, $t(G,v,u)$, to be the average steps until absorption along a random walk terminating at $u$. We define a sea dragon to be a tree with a unique path $P$ such that if $d(u) \geq 3$ for some vertex $u$, then $u \in V(P)$. We use Markov chains to determine $t(G,v,u)$ for all vertices of several classes of sea dragons, a broad subclass of trees. Additionally, we give several results on equations related to ASUAs on general graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23379 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Average Steps until Absorption on Random Walks on Sea Dragon Trees Ates, Lillian Chapman, Zachary Estes, John Jackson, Tyler Combinatorics MCS O5C81, MCS 05C05 For a graph $G$ and vertices $u,v$, we define the ASUA of $v$, $t(G,v,u)$, to be the average steps until absorption along a random walk terminating at $u$. We define a sea dragon to be a tree with a unique path $P$ such that if $d(u) \geq 3$ for some vertex $u$, then $u \in V(P)$. We use Markov chains to determine $t(G,v,u)$ for all vertices of several classes of sea dragons, a broad subclass of trees. Additionally, we give several results on equations related to ASUAs on general graphs. |
| title | Average Steps until Absorption on Random Walks on Sea Dragon Trees |
| topic | Combinatorics MCS O5C81, MCS 05C05 |
| url | https://arxiv.org/abs/2604.23379 |