A lower bound for groupies in graphs

A non-isolated vertex of a graph G is called a groupie if the average degree of the vertices connected to it is larger than or equal to the average degree of the vertices in G. An isolated vertex is a groupie only if all vertices of G are isolated. While it is well known that every graph must contain at least one groupie, the graph Kn − e contains just 2 groupie vertices for n ≥ 2. In this paper we derive a lower bound for the number of groupies which shows, in particular, that any graph with 2 or more vertices must contain at least 2 groupies. © 1996 John Wiley & Sons, Inc.