Graphs with near v- and e-neighbourhoods
Dalibor Fronček · Glasgow Mathematical Journal · 1990
All the graphs considered in this paper are connected finite undirected graphs without loops and multiple edges. By thevertex-neighbourhood (v-neighbourhood)of any vertexxin the graphGwe mean the subgraph induced by the set of all vertices adjacent tox. Analogously by the edge-neighbourhood (e-neighbourhood) of any edgefwith end verticesx, ywe mean the subgraph (f) (or (xy)) induced by the set of all vertices which are adjacent to at least one vertex of the pair x, y and which are different fromx, y.