Fronček, Dalibor Locally linear graphs. (English) Zbl 0664.05054 Math. Slovaca 39, No. 1, 3-6 (1989). 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 Cited in 4 Documents MSC: 05C99 Graph theory Keywords:neighborhood graph; locally linear graphs PDFBibTeX XMLCite \textit{D. Fronček}, Math. Slovaca 39, No. 1, 3--6 (1989; Zbl 0664.05054) Full Text: EuDML 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 [3] SEDLÁČEK J.: Local properties of graphs. (Czech.) Časop. pěst. mat. 106, 1981, 290-298. · Zbl 0478.05080 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.