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On minimal neighbourhood-connected graphs

✍ Scribed by Bert L. Hartnell; William Kocay

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 809 KB
Volume: 92
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90271-3

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✦ Synopsis

Hartnell, B.L. and W. Kocay, On minimal neighbourhood-connected graphs, Discrete Mathematics 92 (1991) 95-105. The closed neighbourhood of a vertex u of a graph G is u* = {v 1 v is adjacent to u} 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 &-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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