Edge-realizable graphs with universal vertices
Dalibor Fronček · Glasgow Mathematical Journal · 1991
All graphs considered in this article are finite connected, without loops and multiple edges. LetGbe a graph andxbe a vertex. The vertex neighbourhood graph (or υ-neighbourhood) ofxinG(denoted by is the subgraph ofGinduced by the set of all vertices ofGadjacent toxAnalogously iff=xyis any edge ofG, the edge neighbourhood graph (ore-neighbourhood) offinGis the subgraph ofG(denoted or induced by the set of all vertices ofGwhich are adjacent to at least one vertex of the pairx, yand are different fromx, y.