Geodesic
Edge-realizable graphs with universal vertices
Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 309-310

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All graphs considered in this article are finite connected, without loops and multiple edges. Let G be a graph and x be a vertex. The vertex neighbourhood graph (or υ-neighbourhood) of x in G (denoted by is the subgraph of G induced by the set of all vertices of G adjacent to x Analogously if f = xy is any edge of G, the edge neighbourhood graph (or e-neighbourhood) of f in G is the subgraph of G (denoted or induced by the set of all vertices of G which are adjacent to at least one vertex of the pair x, y and are different from x, y. 
Fronček, Dalibor. Edge-realizable graphs with universal vertices. Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 309-310. doi: 10.1017/S0017089500008375
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