ON THE LEAST EIGENVALUE OF A GRAPH

Let G be a simple graph with n vertices and λ(G) be the least eigenvalue of G.In this paper, we show that, if G is connected but not complete, then λ(G)≤λ(K~1)and the equality holds if and only if G K~1, where K~1, is the graph obtained by thecoalescence of a complete graph Kof n-1 vertices with a path Pof length one of itsvertices.