- Tytuł:
- On subgraphs with prescribed eccentricities
- Autorzy:
-
Dankelmann, Peter
DeVilbiss, Matthew
Erwin, David J.
Guest, Kelly
Matzke, Ryan - Tematy:
-
distance
eccentricity
subgraph
tree - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/59898577.pdf Link otwiera się w nowym oknie
- Opis:
- A well-known result by Hedetniemi states that for every graph $G$ there is a graph $H$ whose center is $G$. We extend this result by showing under which conditions there exists, for a given graph $G$ in which each vertex $v$ has an integer label $\mathcal{l}(v)$, a graph $H$ containing $G$ as an induced subgraph such that the eccentricity, in $H,$ of every vertex $v$ of $G$ equals $\mathcal{l}(v)$. Such a labelled graph $G$ is said to be eccentric, and strictly eccentric if there exists such a graph $H$ such that no vertex of $H-G$ has the same eccentricity in $H$ as any vertex of $G$. We find necessary and sufficient conditions for a labelled graph to be eccentric and for a forest to be eccentric or strictly eccentric in a tree.
- Dostawca treści:
- Biblioteka Nauki
Artykuł