On minimal neighbourhood-connected graphs
1991; Elsevier BV; Volume: 92; Issue: 1-3 Linguagem: Inglês
10.1016/0012-365x(91)90271-3
ISSN1872-681X
AutoresBert L. Hartnell, William L. Kocay,
Tópico(s)Interconnection Networks and Systems
ResumoThe closed neighbourhood of a vertex u of a graph G is u ∗ = {υ| υ is adjacent to u} ∪ {u} . G is neighbourhood-connected if it is connected, and G − u ∗ is connected but not complete, for all u in G . We consider neighbourhood-connected graphs G for which all G − u ∗ are minimally k -connected, for k = 1, 2, and 3. In particular, we allow G − u ∗ to be a cycle, wheel, or tree, and characterize the graphs G with this property.
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