A note on graphs whose neighborhoods are n-cycles |
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Authors: | Bruce L Chilton Ronald Gould Albert D Polimeni |
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Institution: | 1. State University College, 14063, Fredonia, N.Y., USA
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Abstract: | 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.” It it is the object of this note to provide a list of counter examples to this statement. |
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