摘要
Let G be a simple graph with n vertices and λ<sub>n</sub>（G） be the least eigenvalue of G.In this paper, we show that, if G is connected but not complete, then λ<sub>n</sub>（G）≤λ<sub>n</sub>(K<sub>n-1</sub><sup>1</sup>)and the equality holds if and only if G K<sub>n-1</sub><sup>1</sup>, where K<sub>n-1</sub><sup>1</sup>, is the graph obtained by thecoalescence of a complete graph K<sub>n-1</sub> of n-1 vertices with a path P<sub>2</sub> of length one of itsvertices.
Let G be a simple graph with n vertices and λ_n(G) be the least eigenvalue of G.In this paper, we show that, if G is connected but not complete, then λ_n(G)≤λ_n(K_(n-1)~1)and the equality holds if and only if G K_(n-1)~1, where K_(n-1)~1, is the graph obtained by thecoalescence of a complete graph K_(n-1) of n-1 vertices with a path P_2 of length one of itsvertices.
基金
Research supported by the National Natural Science Foundation of China.
