- Tytuł:
- Tree-Like Partial Hamming Graphs
- Autorzy:
- Gologranc, Tanja
- Powiązania:
- https://bibliotekanauki.pl/articles/30147227.pdf
- Data publikacji:
- 2014-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
partial Hamming graph
expansion procedure
dismantlable graph
gated subgraph
intersection graph - Opis:
- Tree-like partial cubes were introduced in [B. Brešar, W. Imrich, S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory, 23 (2003), 227-240] as a generalization of median graphs. We present some incorrectnesses from that article. In particular we point to a gap in the proof of the theorem about the dismantlability of the cube graph of a tree-like partial cube and give a new proof of that result, which holds also for a bigger class of graphs, so called tree-like partial Hamming graphs. We investigate these graphs and show some results which imply previously-known results on tree-like partial cubes. For instance, we characterize tree-like partial Hamming graphs and prove that every tree-like partial Hamming graph G contains a Hamming graph that is invariant under every automorphism of G. The latter result is a direct consequence of the result about the dismantlability of the intersection graph of maximal Hamming graphs of a tree-like partial Hamming graph.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2014, 34, 1; 137-150
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł