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A note on graphs whose neighborhoods aren-cycles

✍ Scribed by Bruce L. Chilton; Ronald Gould; Albert D. Polimeni

Publisher: Springer
Year: 1974
Tongue: English
Weight: 220 KB
Volume: 3
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00181321

No coin nor oath required. For personal study only.

✦ Synopsis

AnSTRACr. Let G be a graph, and let v be a vertex of G. We denote by N(v) the set of vertices of G which are adjacent to v, and by (N(v)) the subgraph of G induced by N(v).

We call <N(v)) the neighborhood of v. In a paper of 1968, Agakishieva has, as one of her main theorems, the statement: "Graphs in which every neighborhood is an n-cycle exist if and only if 3 ~< n ~< 6.

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