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Locally linear graphs. (English) Zbl 0664.05054

If G is a graph and x is its vertex, then the symbol \(N_ G(x)\) denotes the subgraph of G induced by the set of vertices which are adjacent to x. If \(N_ G(x)\) for each vertex x of G is a regular graph of degree 1, then G is called locally linear. The paper describes fundamental properties of locally linear graphs. Among other results it determines a lower bound and an upper bound for the number of edges of a locally linear graph with a given number of vertices.
Reviewer: B.Zelinka

MSC:

05C99 Graph theory
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References:

[1] ERDÖS P., SIMONOVITS M.: A limit theorem in graph theory. Stud. Sci. Math. Hung. 1, 1966, 51-57. · Zbl 0178.27301
[2] RYJÁČEK Z., ZELINKA B.: A locally disconnected graph with large number of edges. Math. Slovaca, 37, 1987, 195-198. · Zbl 0673.05060
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